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Heatmap on gene expression data:
corrplot(gene_correlation,
method = "circle", #method of the plot, "color" would show colour gradient
tl.col = "black", tl.srt=45, #colour of labels and rotation
col = brewer.pal(n = 8, name ="RdYlBu"), #colour of matrix
order="hclust") #hclust reordering
### Adding correlation coefficients
gene_expr %>%
group_by(EH_ID) %>%
pivot_longer(cols = 8:26, names_to = "Gene", values_to = "gene_expression") %>%
ggplot(aes(x = gene_expression, color = challenge_infection)) +
geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 159 rows containing non-finite values (stat_bin).
gene_expr %>%
group_by(EH_ID) %>%
filter(!challenge_infection == "UNI") %>%
pivot_longer(cols = 8:26, names_to = "Gene", values_to = "gene_expression") %>%
ggplot(aes(x = gene_expression, color = challenge_infection)) +
geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 90 rows containing non-finite values (stat_bin).
summary(gene_expr)
## EH_ID primary_infection challenge_infection infection_history
## Length:116 Length:116 Length:116 Length:116
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## mouse_strain max_WL delta CXCR3_bio
## Length:116 Min. : 73.45 Min. :-12.690 Min. :16.86
## Class :character 1st Qu.: 89.14 1st Qu.: -8.600 1st Qu.:20.08
## Mode :character Median : 94.14 Median : -6.065 Median :21.15
## Mean : 92.37 Mean : -5.065 Mean :21.25
## 3rd Qu.: 97.28 3rd Qu.: -3.741 3rd Qu.:22.57
## Max. :100.00 Max. : 11.610 Max. :25.80
## NA's :6
## IL.6 IL.10 IL.13 IL1RN
## Min. :13.22 Min. :17.79 Min. :14.24 Min. :10.39
## 1st Qu.:19.52 1st Qu.:21.48 1st Qu.:16.11 1st Qu.:14.71
## Median :22.03 Median :23.22 Median :18.64 Median :16.91
## Mean :22.21 Mean :23.24 Mean :18.60 Mean :16.37
## 3rd Qu.:24.97 3rd Qu.:24.85 3rd Qu.:20.56 3rd Qu.:18.21
## Max. :29.95 Max. :29.99 Max. :24.66 Max. :23.14
## NA's :10 NA's :10 NA's :86
## CASP1 CXCL9 IDO1 IRGM1
## Min. :19.96 Min. :10.83 Min. : 8.662 Min. : 7.028
## 1st Qu.:21.28 1st Qu.:14.62 1st Qu.:12.506 1st Qu.: 8.838
## Median :22.62 Median :17.65 Median :15.631 Median : 9.472
## Mean :22.85 Mean :17.74 Mean :15.815 Mean : 9.579
## 3rd Qu.:23.81 3rd Qu.:20.04 3rd Qu.:18.434 3rd Qu.:10.301
## Max. :29.99 Max. :25.74 Max. :27.170 Max. :14.225
## NA's :2
## MPO MUC2 MUC5AC MYD88
## Min. :15.61 Min. : 6.211 Min. : 7.526 Min. : 8.79
## 1st Qu.:17.66 1st Qu.: 7.942 1st Qu.: 9.053 1st Qu.:11.32
## Median :21.50 Median : 8.570 Median :10.101 Median :16.16
## Mean :21.82 Mean : 8.786 Mean :11.598 Mean :16.17
## 3rd Qu.:25.42 3rd Qu.: 9.357 3rd Qu.:12.309 3rd Qu.:19.00
## Max. :29.21 Max. :17.991 Max. :29.918 Max. :28.08
## NA's :15
## NCR1 PRF1 RETNLB SOCS1
## Min. :17.17 Min. :18.08 Min. : 3.437 Min. : 7.087
## 1st Qu.:21.69 1st Qu.:23.49 1st Qu.: 8.444 1st Qu.: 9.675
## Median :23.71 Median :25.39 Median : 9.915 Median :10.466
## Mean :23.50 Mean :25.08 Mean :10.247 Mean :10.606
## 3rd Qu.:25.43 3rd Qu.:27.10 3rd Qu.:11.533 3rd Qu.:11.518
## Max. :29.55 Max. :29.79 Max. :22.021 Max. :15.561
## NA's :10 NA's :23
## TICAM1 TNF Parasite_challenge
## Min. :12.41 Min. :13.79 Length:116
## 1st Qu.:16.51 1st Qu.:19.37 Class :character
## Median :19.12 Median :21.17 Mode :character
## Mean :19.13 Mean :21.43
## 3rd Qu.:21.48 3rd Qu.:23.07
## Max. :29.58 Max. :29.87
## NA's :1 NA's :2
g <- gene_expr
It is possible to compute a pca with missing data using the package missMDA. The missMDA package is dedicated to missing values in exploratory multivariate data analysis: single imputation/multiple imputation, etc.
Following the tutorial of the package author: Francois Husson: https://www.youtube.com/watch?v=OOM8_FH6_8o
Bad methods: removing individuals with missing data or replacing missing data with the mean (default setting in many packages).
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## Warning in PCA(g[8:26]): Missing values are imputed by the mean of the variable:
## you should use the imputePCA function of the missMDA package
#let's do a pca while removing ALL NA values
res.NA.remove <- PCA(g[8:26] %>% na.omit())
# These are rather unsophisticated ways to solve the problem
We will now continue by using an iterative pca to impute missing data A. Initialization: impute using the mean B. Step lampda: # a. do pca on imputed data table S dimensions retained # b. missing data imputed using pca # c. means (and standard deviations) updated C. Iterate the estimation and imputation steps (until convergence) (convergence: the act of converging and especially moving toward union or uniformity)
Overfitting is a common problem due to believing too much in links between variables. –> regularized iterative PCA (This version is what is being implented in missMDA) This is a way of taking less risk when imputing the missing data. The algorithm estimates the missing data values with values that have no influence on the PCA results, i.e., no influence on the coordinates of the individals or variables.
## $Dim.1
## $quanti
## correlation p.value
## IL.13 0.9776601 4.575076e-79
## TNF 0.9206774 2.139356e-48
## IDO1 0.8649672 6.274569e-36
## IL.10 0.8184320 3.355024e-29
## RETNLB 0.8145332 1.001197e-28
## CXCL9 0.7465281 6.676802e-22
## PRF1 0.7402907 2.194441e-21
## TICAM1 0.7333679 7.903732e-21
## NCR1 0.6839699 2.623696e-17
## CXCR3_bio 0.6787540 5.630664e-17
## MYD88 0.6558009 1.356908e-15
## IL.6 0.6172165 1.600776e-13
## IL1RN 0.5396153 4.094022e-10
## MPO 0.3017989 9.933861e-04
## MUC5AC 0.2260973 1.466854e-02
## CASP1 0.2136150 2.131084e-02
## SOCS1 -0.3180971 5.018860e-04
##
## attr(,"class")
## [1] "condes" "list"
##
## $Dim.2
## $quanti
## correlation p.value
## IRGM1 0.7763684 1.339074e-24
## SOCS1 0.6913736 8.632991e-18
## NCR1 0.3780309 2.867164e-05
## TICAM1 0.3744576 3.457090e-05
## MUC2 0.2213188 1.696110e-02
## PRF1 0.2195441 1.788836e-02
## CXCL9 0.2068282 2.590529e-02
## CASP1 -0.3680234 4.815534e-05
## MUC5AC -0.4935210 1.812712e-08
## IL1RN -0.5970273 1.511949e-12
## MPO -0.8303219 1.010067e-30
##
## attr(,"class")
## [1] "condes" "list"
##
## $Dim.3
## $quanti
## correlation p.value
## MUC2 0.8287201 1.644715e-30
## CASP1 0.7881238 8.851803e-26
## MUC5AC 0.6523399 2.141080e-15
## SOCS1 0.5260068 1.330377e-09
## IRGM1 0.4484578 4.452910e-07
## CXCR3_bio 0.2532317 6.093521e-03
## MYD88 0.2141508 2.097999e-02
## CXCL9 -0.1993732 3.190083e-02
## TICAM1 -0.2244631 1.542027e-02
##
## attr(,"class")
## [1] "condes" "list"
##
## $call
## $call$num.var
## [1] 1
##
## $call$proba
## [1] 0.05
##
## $call$weights
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [112] 1 1 1 1 1
##
## $call$X
## Dim.1 CXCR3_bio IL.6 IL.10 IL.13 IL1RN CASP1
## 1 -0.915545774 20.92666 21.09045 21.78837 18.20471 16.42338 22.02920
## 2 0.011780083 21.62075 25.32600 22.92255 19.01956 20.13510 24.25054
## 3 1.584363191 23.66537 24.18021 24.90025 20.31376 18.14916 22.55511
## 4 -1.818030087 20.21312 23.90781 22.31029 17.23688 16.79377 27.50341
## 5 2.034804392 23.02829 23.19571 27.67319 20.87536 18.98532 25.45624
## 6 2.832029262 23.18574 22.59572 25.82543 21.46693 19.45825 23.14097
## 7 -0.570846800 20.19632 23.91450 21.62915 18.46942 18.55582 23.11127
## 8 0.809533133 23.73105 21.14346 23.61026 19.35098 17.67666 25.06357
## 9 1.765621773 23.18462 22.02135 24.86233 20.33561 19.31653 22.45011
## 10 -3.291836424 19.21698 19.62519 22.94861 15.86227 17.29027 23.55407
## 11 2.011495300 22.52077 23.46206 23.85751 20.85859 20.58918 23.81598
## 12 -3.125533593 19.12177 25.26331 20.62422 16.15499 17.38254 22.70095
## 13 0.054794456 22.45032 22.69335 23.62850 18.93492 17.74972 22.49518
## 14 -0.372270923 22.51152 20.95665 23.01596 18.52967 16.69397 22.84267
## 15 0.775923951 21.26747 21.85538 23.82383 19.73429 19.67336 22.04784
## 16 -3.512223468 18.00746 18.38914 18.74826 15.90985 15.10803 23.38067
## 17 -2.001392829 19.10121 20.98553 22.42743 17.18706 16.44270 23.42149
## 18 1.660922890 22.41295 20.25383 23.03015 20.32417 17.63167 22.85872
## 19 -0.966654087 21.44775 18.45020 27.89777 17.76739 17.32784 23.05298
## 20 -1.864788567 21.07130 20.03526 21.08242 17.11006 17.43922 22.51961
## 21 -1.007482453 20.92691 21.09167 24.07971 17.98829 17.14403 22.76425
## 22 -3.584868773 19.36417 15.07182 20.66591 15.58336 16.54046 24.16598
## 23 -3.678212445 18.14328 17.39709 21.31080 15.58911 12.63218 23.57993
## 24 -0.841502706 20.03795 28.89199 21.07542 18.86096 18.66006 29.94250
## 25 1.500264009 23.44335 23.78059 24.23830 20.61809 16.75777 23.76993
## 26 -1.926479521 20.31368 19.93494 21.62254 17.14027 17.64324 22.86814
## 27 3.113068945 24.81556 21.68421 25.12770 21.75416 18.20610 22.86023
## 28 0.092018252 20.53629 25.89126 23.68561 19.46835 16.66748 28.45142
## 29 -0.742775277 20.53802 20.02823 20.76649 18.13779 17.42489 22.69451
## 30 -4.195983201 18.97607 19.07150 21.15728 14.99924 13.40232 24.16373
## 31 0.607274587 23.27692 19.71861 23.52992 19.56396 19.58139 21.79801
## 32 -0.002842419 21.66393 20.33407 20.44784 19.29409 17.72250 23.41526
## 33 0.778082720 23.07634 22.39279 23.94323 19.60995 19.91583 23.28426
## 34 -0.520873430 22.53733 18.60527 22.20044 18.41209 17.97018 25.19149
## 35 0.799691732 22.10287 20.06929 24.09205 19.58568 19.46909 21.63034
## 36 1.575786400 24.60278 18.46774 26.19512 20.22045 19.76563 23.74273
## 37 -3.860247890 18.58505 19.05836 17.86940 15.74421 14.97143 20.93711
## 38 -6.674900348 16.86408 13.21835 17.79117 12.78276 14.25306 24.43256
## 39 -0.809016843 22.15447 25.41724 22.04275 18.16404 17.18358 29.98603
## 40 -0.853391090 21.16552 18.10097 22.65766 18.21368 17.71976 24.28977
## 41 0.367541349 24.69742 19.05980 23.16757 19.17256 18.98606 22.78772
## 42 0.728066595 21.32868 21.65526 24.18590 19.50128 17.83004 22.53197
## 43 -5.040384134 18.70600 17.79219 18.49236 14.33358 14.68719 24.20202
## 44 0.848172054 22.12217 21.87536 23.32834 19.85906 18.26465 23.79661
## 45 -4.500887228 19.16785 17.97426 19.89393 14.81195 15.60916 23.59150
## 46 -3.819212366 18.19756 14.40759 20.83681 15.46550 17.24873 25.16027
## 47 -2.043532059 21.64540 17.73381 20.98086 16.94110 17.40872 20.43007
## 48 -3.090244335 20.18662 16.57967 19.05747 16.20012 16.32045 22.82450
## 49 -3.974399445 18.21390 29.81903 18.33959 15.70261 13.28305 25.93133
## 50 0.868149879 20.61515 23.03621 29.98877 19.87497 12.75221 20.43024
## 51 1.528209216 21.00294 23.67766 24.20689 20.54626 15.08824 20.90917
## 52 -1.484400934 20.65725 21.54047 23.25961 17.66527 11.65156 22.92319
## 53 1.895868415 21.31698 26.71171 25.52867 20.96153 13.83283 21.43852
## 54 -0.847813440 20.20715 24.37765 22.34004 18.42687 11.97324 21.03117
## 55 -3.501222446 18.40655 21.07280 21.44767 15.95547 11.82725 21.70017
## 56 -0.561376714 20.89049 23.48067 22.36207 18.55236 11.85427 21.44578
## 57 0.066074387 21.14188 24.07659 23.60720 19.22818 13.10425 25.34167
## 58 1.517001465 21.95768 22.34438 26.11948 20.51676 15.37061 21.28205
## 59 -2.701493670 18.21933 25.24031 20.51353 16.79688 12.28923 22.26009
## 60 0.399702758 24.65157 23.53264 23.43752 19.37199 11.43627 25.73564
## 61 0.421502299 23.52242 27.13311 24.12098 19.47855 11.27634 21.92730
## 62 5.393204085 22.91576 25.39795 28.87344 23.88989 16.75650 22.16068
## 63 5.889680025 25.66519 26.11602 27.58330 24.25735 19.70521 26.08998
## 64 7.098575665 24.22064 29.76292 28.05381 25.62352 19.23186 27.75083
## 65 3.982560186 22.86653 23.56129 25.01750 22.69070 18.03112 21.69953
## 66 4.281134917 22.76071 26.78894 27.95595 23.15535 15.84708 23.58463
## 67 6.831011961 23.52785 29.95433 28.18004 25.45059 23.13962 27.11709
## 68 5.540614286 22.75096 27.96307 25.69999 24.20575 17.58811 23.01611
## 69 3.611356503 21.48844 22.60560 29.13131 22.36904 18.63039 20.75492
## 70 7.596823857 25.80037 29.77186 29.09962 26.17544 20.02498 26.91510
## 71 2.874537418 21.03955 26.23716 26.44454 21.73347 16.61041 22.30920
## 72 4.795566060 21.52073 27.46334 24.91564 23.29033 17.10527 24.02626
## 73 4.537132227 22.66652 18.92939 25.56209 22.76709 18.86001 24.83386
## 74 -0.593108710 21.81679 20.56615 26.30993 18.24177 12.25711 21.65407
## 75 6.716558268 22.67323 26.18491 27.22396 25.27947 20.08638 25.34344
## 76 3.517995949 23.46890 22.68031 23.16663 22.11858 18.06204 22.36512
## 77 -1.779229385 19.91255 22.64689 22.45926 17.54585 11.27495 21.54675
## 78 -2.054941315 20.08603 21.31040 22.15091 17.23761 10.39335 20.70334
## 79 4.392302673 24.06576 28.75247 23.54490 23.10769 21.42000 27.75544
## 80 -1.386659442 21.27995 18.29274 24.38039 17.57979 12.06338 20.29093
## 81 -2.636669055 20.22281 24.09667 19.95704 16.75355 12.45559 21.84692
## 82 1.498389308 24.54876 23.94933 25.98836 20.62077 14.72332 24.56166
## 83 1.486028669 19.66524 28.21305 25.28405 20.68618 12.24016 21.28489
## 84 1.002576368 21.37939 22.23118 24.59390 20.11525 17.24273 21.67512
## 85 -1.609344620 20.76001 22.04766 22.25595 17.53079 15.60735 20.92126
## 86 -1.014946561 18.55728 25.20569 24.22079 18.42338 15.59951 19.99790
## 87 3.064475490 20.76581 23.12287 24.20175 24.65534 16.35892 21.11699
## 88 -0.287117840 19.80003 24.82849 24.68163 18.29073 12.63565 23.09224
## 89 -0.125845513 20.95861 24.47956 26.12950 20.04791 11.69210 22.80543
## 90 -0.409897637 21.59717 26.58406 21.70019 21.35713 11.07716 20.93479
## 91 -2.832695773 18.34869 21.28534 21.67449 15.43664 14.73684 19.96002
## 92 -0.496023933 21.69704 25.01886 23.22688 17.92247 15.92684 21.19813
## 93 -0.437785486 21.45424 19.31163 23.59355 18.98706 18.17187 22.41502
## 94 -5.684911320 19.13856 16.59937 17.90145 14.23954 12.16899 21.02919
## 95 0.192036635 20.68170 26.84019 24.26723 19.69519 17.50911 20.48537
## 96 1.043987030 18.54700 25.63743 23.37539 20.64206 17.68361 21.37431
## 97 -0.913418070 20.46746 18.96176 24.76140 17.74507 17.02771 20.42448
## 98 -0.008433619 19.20522 21.60006 22.75786 19.52374 19.51251 20.75696
## 99 -1.770740100 21.53098 18.24249 22.16032 17.34487 13.69251 24.61451
## 100 1.668914450 20.54109 26.92355 21.56791 22.61048 20.05260 24.82729
## 101 -1.991726509 20.32615 23.60529 21.83610 16.52889 15.60828 20.62177
## 102 -2.078620987 20.58743 22.64934 21.05282 15.64012 15.78011 21.04427
## 103 -2.075698591 21.30977 24.81393 20.53981 15.96387 15.62994 22.11439
## 104 0.017283801 24.78347 20.20337 23.52439 19.78487 14.97696 22.93029
## 105 2.711804234 22.77867 25.05195 25.24735 23.10120 20.21300 25.57550
## 106 -3.650027373 20.05828 17.73281 19.67574 14.96183 14.91150 20.39827
## 107 -2.917951946 20.06144 19.48198 22.33842 15.84020 15.91221 20.98834
## 108 -2.940622156 21.33039 19.22344 21.16372 16.83008 12.50428 22.24713
## 109 -2.725183539 21.08006 18.49392 19.74151 15.73607 12.83904 21.46682
## 110 1.495490699 18.95654 21.82732 26.77299 21.41995 19.69194 20.78469
## 111 1.879367204 20.24860 28.76398 23.93211 21.10862 20.95269 21.23007
## 112 0.873089477 19.01495 26.92797 23.32124 20.67509 18.21358 20.67898
## 113 -0.884056174 22.14929 22.09470 24.41267 16.81424 17.08754 20.84055
## 114 -4.035682818 23.41073 17.46569 19.79551 14.49658 13.13472 25.08039
## 115 0.791002902 18.84797 25.09494 24.87735 20.31023 15.62935 20.16156
## 116 0.612760349 21.05519 27.11805 23.21401 20.25871 18.40590 21.07134
## CXCL9 IDO1 IRGM1 MPO MUC2 MUC5AC MYD88
## 1 13.60226 13.685507 11.625516 23.16109 11.394231 12.368312 16.856985
## 2 14.53048 12.347823 10.033986 26.67972 9.724516 14.599135 18.010443
## 3 18.99093 15.902410 7.810604 25.81143 7.749293 12.871210 20.059938
## 4 14.03929 12.783337 10.157602 27.67628 7.183272 14.041496 15.618948
## 5 19.20542 18.254268 9.241544 26.30798 9.869590 14.371520 17.538455
## 6 19.07817 18.488880 9.197374 24.94612 8.225922 11.583533 20.053889
## 7 14.67773 14.430931 8.600942 24.90775 8.730690 11.900492 18.177256
## 8 14.21946 15.666291 8.297135 25.61896 7.522414 13.148207 19.038180
## 9 16.20309 14.952342 8.997360 29.21133 8.156661 8.684992 20.392755
## 10 12.88829 11.663551 9.052160 27.46451 8.642571 10.342714 14.618691
## 11 20.30617 16.930006 8.162201 25.54124 8.859693 15.460500 19.281729
## 12 13.01806 10.705361 7.565302 24.91439 6.904949 15.359870 14.612337
## 13 17.39209 15.675249 9.841508 25.19862 7.871219 8.678551 16.285136
## 14 15.54217 13.079090 10.548003 23.12428 9.808142 10.449504 16.981842
## 15 19.29231 18.558979 9.218357 28.14862 8.669347 10.198480 16.960683
## 16 17.12064 15.731242 9.193427 23.38627 8.394537 10.196126 14.609839
## 17 13.68531 12.914861 9.322633 21.87048 8.714876 12.295662 15.888646
## 18 18.63569 19.069602 9.447187 27.92150 8.040773 9.121950 17.378285
## 19 12.95849 14.508282 9.598510 27.07087 7.807939 10.415893 15.854892
## 20 14.61636 13.138920 8.335187 24.66545 7.790361 9.038129 16.616529
## 21 16.18053 13.646650 9.565223 25.42206 8.771323 9.468288 15.065539
## 22 15.03703 16.004009 8.438642 27.97673 8.473955 10.951688 12.671592
## 23 14.00879 11.186614 9.439790 24.48003 8.613752 20.293679 13.916375
## 24 14.61884 12.098614 8.954314 24.31267 17.990707 24.237810 15.120134
## 25 21.33524 18.017771 11.480787 19.99031 10.255215 10.923709 17.310957
## 26 16.94201 12.246575 8.748695 26.20443 7.940369 12.292991 15.518893
## 27 18.99404 18.253549 10.577026 24.31717 8.761090 9.023115 19.547397
## 28 16.56531 16.273956 13.691213 20.56654 12.038068 20.929919 15.678849
## 29 15.85200 12.968113 8.203141 26.76613 8.233775 17.425917 17.354687
## 30 13.93241 11.229936 9.725386 24.64733 6.814177 11.003653 13.408224
## 31 18.71677 17.629490 10.881357 25.72409 10.267396 11.219287 15.989496
## 32 19.96504 19.114217 11.739965 21.94526 12.198908 12.960735 16.747558
## 33 18.19233 16.734890 8.942380 24.38990 8.418066 9.847442 16.538393
## 34 18.54367 17.279974 9.036738 22.05586 7.435172 13.026381 16.057834
## 35 17.56039 18.416046 8.848435 25.72081 8.204233 9.882749 18.079438
## 36 18.40169 19.753084 9.752966 28.66910 9.577180 10.404196 17.139011
## 37 16.51682 16.471883 11.495214 20.75777 10.413618 11.989536 14.774482
## 38 13.82651 8.661838 7.154126 23.86028 7.951477 15.116064 10.230339
## 39 13.24525 13.915862 8.987010 27.49619 9.597302 21.741745 16.270490
## 40 17.31654 17.871126 10.481867 23.27109 9.326657 9.908069 15.881726
## 41 18.82635 17.110750 10.481346 24.32100 8.573053 9.253118 16.642453
## 42 17.26648 15.929076 8.958850 24.41816 7.632720 8.440455 19.807910
## 43 12.21244 9.754557 9.836893 23.37686 9.851718 11.585622 14.407068
## 44 20.24753 19.708596 9.977461 24.92838 8.415812 8.076470 17.337172
## 45 13.56512 9.842353 9.029007 24.40325 9.316026 9.889951 13.850419
## 46 16.38290 15.927925 8.049613 26.94072 7.563250 12.350998 11.128010
## 47 16.55790 15.251946 9.385581 27.61566 8.563067 9.972695 15.725963
## 48 17.97308 18.265865 9.486106 23.34994 7.878306 10.787435 12.493822
## 49 11.98283 10.025161 8.136754 27.16886 10.834516 29.918079 13.929742
## 50 18.32872 16.717158 10.030781 16.37685 8.541946 8.852514 20.404963
## 51 21.96734 18.171699 9.531294 15.92918 7.957801 8.211709 24.785884
## 52 16.90758 12.292333 11.168791 17.07884 8.345124 10.313463 15.319679
## 53 22.16466 18.373123 9.563630 16.38449 8.132526 8.572920 23.240718
## 54 16.66383 11.993194 11.576390 17.15236 10.280913 10.532018 18.139879
## 55 15.42738 12.523361 9.928879 16.55492 8.291121 9.120236 13.839477
## 56 16.72246 13.721075 10.479662 16.32184 8.641474 8.817069 19.929199
## 57 18.64811 15.843818 10.788702 17.07038 9.428260 9.364003 18.078884
## 58 22.49707 18.930756 8.050492 16.71614 7.611355 7.888725 20.995390
## 59 15.25164 11.803676 10.108555 16.57170 9.364101 9.848285 15.544608
## 60 20.65578 12.237259 11.398526 16.60661 9.628627 9.639826 19.190942
## 61 18.51135 13.708155 10.256888 16.39160 9.063478 9.058345 20.478204
## 62 23.45426 21.459525 7.149357 25.63594 6.211322 10.154484 24.906656
## 63 19.96006 20.724537 9.016223 26.44495 9.246984 14.123916 24.948713
## 64 23.07473 27.169505 8.986193 27.97227 8.883982 23.694956 27.782637
## 65 24.18800 22.517576 8.747040 26.39468 7.865111 9.540464 19.913584
## 66 23.33492 22.130637 9.505613 20.34651 9.117813 10.210623 25.644537
## 67 22.51919 24.362430 7.028294 31.62038 9.249620 25.681823 23.705403
## 68 24.12845 22.364820 7.679259 28.01318 7.529806 12.495365 24.056632
## 69 22.14808 21.229097 8.823074 24.08935 7.071763 8.979468 18.841489
## 70 23.73669 26.746953 10.566932 23.76439 10.301982 15.246147 24.071985
## 71 20.71644 20.531902 8.015308 26.53156 6.875894 15.616582 18.824360
## 72 18.86451 21.448918 7.324264 27.47612 6.626930 13.267206 25.219254
## 73 16.34429 22.097978 7.796770 29.42759 8.052046 18.066238 24.484515
## 74 13.14677 13.300336 10.259382 16.46249 8.504597 8.874519 20.875416
## 75 23.74179 25.029717 9.255368 27.99719 8.579815 29.113148 28.078962
## 76 19.88270 20.563533 10.008556 23.69222 8.371019 9.336553 24.674035
## 77 18.09229 12.713460 10.729052 16.12279 9.020236 9.326122 17.670409
## 78 18.47461 11.083212 9.706705 15.60862 8.225850 8.669181 17.396433
## 79 18.54329 18.841289 7.212158 28.72646 11.580169 26.744894 20.536848
## 80 14.49042 12.360175 10.292874 16.43850 8.630854 8.630570 17.291781
## 81 14.45594 11.304476 9.925298 17.66268 9.721816 10.491249 15.854700
## 82 22.72566 15.063209 14.224817 20.66631 12.365167 12.636119 18.984608
## 83 23.29208 13.730573 11.186153 16.54841 9.411632 9.773155 28.008621
## 84 19.01887 18.925460 10.323671 17.42215 8.655927 9.526401 18.953311
## 85 14.94362 12.729950 9.898791 17.78050 8.541098 8.728032 16.724469
## 86 18.02023 16.255302 10.261519 17.17013 8.567059 8.840712 17.923550
## 87 21.25767 21.997595 7.290380 28.70681 6.445662 9.138264 13.951069
## 88 20.79058 13.061516 11.602668 17.49598 9.719942 10.305993 10.797975
## 89 21.78558 12.274416 11.183381 17.01788 9.354890 9.778690 10.666151
## 90 22.47699 11.437480 10.668408 16.28529 8.850896 9.096841 10.200785
## 91 15.04185 13.407077 9.601861 16.79333 7.966876 8.117302 9.107979
## 92 18.33013 15.595453 9.425018 16.97132 7.794905 8.401166 9.336994
## 93 14.38687 12.455074 9.436140 24.79474 8.197041 9.244237 9.956077
## 94 10.82695 9.136530 9.375088 17.69353 8.866534 9.777502 10.271472
## 95 18.70781 14.946433 8.839694 19.82217 7.487277 8.125193 8.844189
## 96 24.86841 19.502043 9.457993 18.28340 8.071410 8.206934 9.252441
## 97 15.35375 14.252057 9.304423 23.43023 7.997043 9.088218 9.269372
## 98 18.79592 16.970430 8.739251 20.15552 9.256436 10.444694 10.814310
## 99 14.09206 12.763815 12.235026 19.78562 11.179115 11.697763 12.527439
## 100 18.86993 17.037959 10.412347 19.15029 9.342203 9.990472 11.061339
## 101 13.72277 12.100585 8.635025 19.64736 7.290007 8.052774 8.988102
## 102 14.14905 14.815813 9.722631 18.87126 8.935368 10.212263 10.256080
## 103 14.05901 11.611228 8.832139 17.72639 7.722895 8.278575 9.471053
## 104 16.14029 14.976568 10.745571 18.11004 9.538819 10.048293 10.673092
## 105 21.90772 20.337306 10.781881 19.84596 9.299197 9.821379 10.803154
## 106 12.87900 11.674964 8.890484 21.49815 8.237312 8.762589 9.752521
## 107 11.55303 11.659147 9.496184 20.05410 7.969417 8.572635 9.429172
## 108 15.30404 11.142649 11.492399 18.39825 10.125236 10.724162 11.321831
## 109 13.54572 11.447434 10.481360 18.73255 9.916628 10.691091 11.307609
## 110 25.69238 20.921377 9.314263 19.02520 8.686559 9.464939 10.506455
## 111 25.34770 20.689122 8.418992 24.76759 7.942093 9.095062 9.772552
## 112 25.74388 20.553644 8.419839 21.41300 6.748056 7.525599 8.790171
## 113 15.14489 15.490731 9.344918 21.30055 7.847138 8.507111 9.580745
## 114 12.26390 8.769283 10.113600 19.62256 10.336654 11.690665 10.798740
## 115 20.93232 18.051913 9.677846 16.56573 7.916451 8.172702 9.524207
## 116 17.73318 16.366598 8.701905 20.94546 7.665722 8.340444 9.444841
## NCR1 PRF1 RETNLB SOCS1 TICAM1 TNF
## 1 23.33234 27.53290 11.389996 13.025961 19.82281 21.01065
## 2 22.89312 26.26383 7.857130 10.292493 17.66099 22.36282
## 3 23.96486 25.98379 9.184355 9.205008 19.11736 22.81213
## 4 23.45405 23.24062 3.920192 10.692568 15.46167 18.96024
## 5 24.12714 27.09015 8.711133 10.586118 17.03506 24.77639
## 6 25.43377 27.84301 15.803676 10.037031 18.92915 25.01909
## 7 23.25482 23.54348 11.930951 10.137282 17.89026 20.40686
## 8 23.69673 28.00436 10.795116 10.187464 17.98634 21.91510
## 9 23.81112 27.02770 11.763447 9.833251 20.04689 25.99834
## 10 21.39968 20.45141 4.079604 11.242170 15.12650 18.21831
## 11 23.66060 26.21540 12.512554 8.390115 17.00279 24.39284
## 12 20.06957 21.01384 3.598778 8.892853 14.34632 18.18376
## 13 24.37670 25.10224 11.645965 10.674034 15.64940 20.93638
## 14 23.76296 27.17679 12.534258 11.718299 17.56715 20.51972
## 15 23.89841 24.64252 11.212956 10.034478 16.84957 22.49043
## 16 18.00615 22.71284 6.937463 10.044808 15.08446 17.05868
## 17 21.33841 26.20900 5.973854 10.589004 17.65482 19.35511
## 18 29.49340 25.66098 14.362461 10.790189 18.71333 23.10196
## 19 23.12706 25.41527 5.662282 10.323638 15.91257 19.63243
## 20 22.28476 23.09671 6.708141 9.097796 16.83769 19.32845
## 21 24.36829 25.16968 8.373846 10.727382 15.39051 19.76802
## 22 18.33988 22.09717 3.437346 10.438836 13.27494 18.82194
## 23 18.49862 22.59840 4.203089 9.684278 13.27406 22.08087
## 24 20.80061 24.78750 4.605416 10.017204 15.04402 23.69131
## 25 25.28210 25.69449 9.644582 12.041930 19.34746 26.10923
## 26 20.79229 26.11614 6.063100 9.980612 14.75829 18.44981
## 27 23.63638 28.71855 12.795983 9.838008 22.32244 29.87482
## 28 22.63025 28.71924 13.919183 15.560557 16.95622 20.43844
## 29 21.23689 29.16415 9.982388 9.482890 14.86344 21.08135
## 30 20.03371 21.10798 5.917482 11.194286 13.04953 16.84558
## 31 20.77055 28.50238 10.511800 11.429176 16.45653 24.00758
## 32 20.53246 29.53929 10.842803 12.155859 17.76277 21.50840
## 33 25.24495 25.38933 11.824440 9.660671 15.41369 20.83225
## 34 21.49756 25.56295 7.036342 8.830993 15.62009 20.40643
## 35 22.91124 26.37404 12.132540 9.535813 16.56348 22.45497
## 36 21.85548 28.15420 9.879838 11.097173 16.94929 24.08582
## 37 19.67674 21.14482 8.466972 12.429422 15.73371 16.46384
## 38 17.36359 18.08027 3.785109 10.974022 12.41300 13.78664
## 39 23.07639 24.78306 5.259263 10.307205 14.37050 19.70445
## 40 19.59789 26.08224 11.495341 11.487913 16.29785 20.60002
## 41 22.90715 27.33195 7.758496 11.493739 17.45863 22.01304
## 42 24.18657 29.51591 9.225770 9.632405 17.44476 21.63822
## 43 19.93898 20.38618 4.346449 11.657992 15.33566 15.86004
## 44 21.63473 28.11725 9.187486 10.970666 19.30253 21.39020
## 45 18.81508 21.15985 4.867295 11.106637 15.25927 16.16250
## 46 17.17266 21.54708 3.690941 10.228503 13.47368 18.09514
## 47 21.39350 23.41759 8.189116 10.139407 15.24493 17.65270
## 48 17.79122 25.89262 4.204721 10.569843 12.91764 17.50383
## 49 18.11990 19.92611 3.577107 10.324091 14.54200 16.01331
## 50 25.36659 26.01465 10.749170 11.024760 21.19794 21.01304
## 51 26.75319 27.09819 9.755923 10.478270 22.50241 21.56508
## 52 24.26265 27.12899 10.841208 12.989070 16.99448 20.03119
## 53 27.48604 27.18535 9.478791 10.607035 21.82549 21.98348
## 54 26.70705 25.41207 12.030827 13.123553 21.09282 21.07389
## 55 20.19892 21.79024 9.145387 10.833533 15.29784 19.01250
## 56 25.53460 26.41866 9.278296 11.303618 21.34152 21.31616
## 57 26.75811 25.29939 9.923647 11.828319 19.06670 21.78523
## 58 23.38357 26.14829 8.262385 8.890513 20.80948 23.70044
## 59 22.93460 25.11673 9.047844 11.867247 16.30778 18.36694
## 60 23.87387 28.88317 9.635853 12.837053 19.15818 22.89580
## 61 26.26590 23.85662 9.703631 11.627023 21.52452 22.65241
## 62 27.00035 27.90638 18.572389 8.318661 29.57724 23.13135
## 63 27.56776 29.56682 17.913556 10.084373 25.58661 27.81593
## 64 25.83862 27.59474 20.897073 9.482244 24.73153 27.59754
## 65 29.07498 28.19561 16.332964 9.665532 21.42768 23.91542
## 66 26.89351 28.51895 9.493187 11.330597 26.12898 26.67485
## 67 25.96444 28.22388 14.714598 8.041715 24.10520 28.93255
## 68 25.88560 25.43324 20.720319 7.087203 26.26861 27.69078
## 69 26.76586 28.06315 10.975465 9.162248 19.60484 29.13404
## 70 28.71996 31.76473 22.021335 13.581984 25.64584 28.37664
## 71 24.66802 26.78273 13.342864 8.919463 19.84097 25.19713
## 72 27.21686 26.69613 20.083060 7.158283 23.30618 28.17372
## 73 24.82501 28.62742 22.004654 8.871887 23.74250 28.31769
## 74 24.39808 26.19344 9.526062 11.755902 21.52548 20.79691
## 75 27.33835 28.89657 18.031914 9.895583 25.98677 28.62975
## 76 25.71248 29.79103 15.178442 10.393341 22.46358 27.50077
## 77 22.21427 25.55363 9.661429 12.013956 18.22035 19.84642
## 78 22.32535 24.21456 8.805372 11.222371 20.81727 19.51511
## 79 28.81700 26.48781 16.855267 8.065261 20.60755 23.72752
## 80 24.59491 26.21215 9.441200 11.032251 20.47256 20.23849
## 81 22.79706 23.15837 9.722345 12.451737 20.65242 17.12110
## 82 25.50603 26.79236 13.220426 14.919748 20.57782 22.50920
## 83 26.55833 27.50508 10.058471 12.308402 22.04861 23.31357
## 84 27.12947 24.06304 10.004453 11.728596 24.10621 21.72844
## 85 24.81094 23.62678 9.365788 11.073955 17.51909 19.97281
## 86 22.33892 23.77440 9.192797 11.689073 18.09591 20.75239
## 87 23.72726 23.93945 15.923781 7.757090 27.17214 25.43076
## 88 25.57028 25.88464 11.281775 12.009186 21.10553 22.98131
## 89 24.28717 25.98337 10.982572 12.330284 20.82249 21.80276
## 90 23.38032 25.16243 10.944685 11.589537 23.26258 20.96380
## 91 22.97322 27.10505 8.885230 11.076750 16.22269 18.16059
## 92 24.09515 24.29967 10.008384 10.705349 22.69601 20.23189
## 93 26.18841 25.49433 10.995071 10.401308 20.49431 21.47300
## 94 19.15281 19.06725 7.547668 11.758377 17.68614 16.26408
## 95 23.92244 25.49845 9.999622 9.756697 21.55859 21.56077
## 96 25.46251 26.64396 9.906633 10.453336 22.37117 22.84888
## 97 22.09169 28.07379 9.665312 9.605007 20.07661 20.12716
## 98 26.34456 23.49281 9.661908 9.225406 21.56845 22.03168
## 99 24.33736 23.94627 12.576263 12.867410 20.08692 20.32090
## 100 24.35790 24.18033 11.724569 10.427714 27.52816 26.40631
## 101 26.30723 23.92448 7.985537 9.284697 19.19948 18.33022
## 102 22.18252 28.09646 5.846103 10.089456 18.04099 19.42994
## 103 26.67078 22.17432 8.544338 9.708748 19.40001 18.85483
## 104 24.40765 25.97794 11.387807 11.285548 22.13123 21.26313
## 105 24.99690 28.24536 10.488427 11.445105 22.62902 25.72357
## 106 21.39041 22.26847 10.541307 9.678177 16.57747 17.42194
## 107 23.67079 24.50357 8.477857 10.166476 17.26136 17.46136
## 108 19.99873 23.04488 10.740533 11.861010 20.43164 17.80555
## 109 29.54948 22.51975 10.484425 12.108359 20.85134 16.34527
## 110 23.17187 25.18772 11.220518 9.548208 22.43535 22.25967
## 111 21.21622 24.28532 10.960531 8.968065 23.16068 23.48999
## 112 22.99591 24.24964 10.019037 8.531568 21.37614 20.82249
## 113 25.42788 24.87718 8.590075 8.871211 17.57769 19.73392
## 114 23.75737 20.88617 6.927890 13.408973 17.53509 16.57800
## 115 26.10599 28.46406 10.098975 10.393635 23.04097 22.15808
## 116 24.42321 27.33021 10.388094 8.474758 19.93831 21.28205
Caution: When imputing data, the percentages of inertia associated with the first dimensions will be overestimated.
Another problem: the imputed data are, when the pca is performed considered like real observations. But they are estimations!!
Visualizing uncertainty due to issing data:
–> mulrimple imputation: generate several plausible values for each missing data point
We here visualize the variability, that is uncertainty on the plane
defined by two pca axes.
## $PlotIndProc
##
## $PlotDim
##
## $PlotIndSupp
##
## $PlotVar
Individuals lying on the axis have no missing data, but individuals that
far away have many missing data. big ellipse = big uncertainty tight
elipse (line) = low uncertainty
Variable representation: Poins tight together )look like one) - have no missing variables –> low uncertainty Points spread – > higher variability – > higher uncertainty
High uncertainty–> we should interpret the result with care
The individuals with many missing data values make the axes move, and thus the positions of all individuals
Therefore in the last plots every individual is getting an eclipse as they are as well influenced by the missing data of the others.
THe plot with the dimensions shows the projections of the pca dimensions of each imputed table on the pca plane obtained using the original imputed data table
As all of the arrows are close to either the first or second axes, this means that the axes are stable with respect to the set of imputed tables –> we don’t have evidence of instability here.
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
##
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
##
## select
##
## Attaching package: 'reshape2'
## The following object is masked from 'package:tidyr':
##
## smiths
The function fviz_contrib() [factoextra package] can be used to draw
a bar plot of variable contributions. If your data contains many
variables, you can decide to show only the top contributing variables.
The R code below shows the top 10 variables contributing to the
principal components:
The total contribution to PC1 and PC2 is obtained with the following R
code:
The red dashed line on the graph above indicates the expected average
contribution. If the contribution of the variables were uniform, the
expected value would be 1/length(variables) = 1/10 = 10%. For a given
component, a variable with a contribution larger than this cutoff could
be considered as important in contributing to the component.
Note that, the total contribution of a given variable, on explaining the variations retained by two principal components, say PC1 and PC2, is calculated as contrib = [(C1 * Eig1) + (C2 * Eig2)]/(Eig1 + Eig2), where
C1 and C2 are the contributions of the variable on PC1 and PC2, respectively Eig1 and Eig2 are the eigenvalues of PC1 and PC2, respectively. Recall that eigenvalues measure the amount of variation retained by each PC. In this case, the expected average contribution (cutoff) is calculated as follow: As mentioned above, if the contributions of the 10 variables were uniform, the expected average contribution on a given PC would be 1/10 = 10%. The expected average contribution of a variable for PC1 and PC2 is : [(10* Eig1) + (10 * Eig2)]/(Eig1 + Eig2)
To visualize the contribution of individuals to the first two principal
components, type this:
PCA + Biplot combination
In the following example, we want to color both individuals and
variables by groups. The trick is to use pointshape = 21 for individual
points. This particular point shape can be filled by a color using the
argument fill.ind. The border line color of individual points is set to
“black” using col.ind. To color variable by groups, the argument col.var
will be used.
To customize individuals and variable colors, we use the helper functions fill_palette() and color_palette() [in ggpubr package].
##
## Call:
## lm(formula = max_WL ~ pc1 + pc2 + challenge_infection, data = g)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.4027 -3.0794 0.1195 3.5224 14.2423
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 91.7467 0.7956 115.324 < 2e-16 ***
## pc1 0.1173 0.1829 0.641 0.522840
## pc2 -0.7231 0.2842 -2.544 0.012337 *
## challenge_infectionE88 -6.1131 1.4142 -4.323 3.38e-05 ***
## challenge_infectionUNI 4.4111 1.1359 3.883 0.000175 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.258 on 111 degrees of freedom
## Multiple R-squared: 0.3805, Adjusted R-squared: 0.3582
## F-statistic: 17.04 on 4 and 111 DF, p-value: 6.364e-11
## [1] 721.1667
##
## Call:
## lm(formula = max_WL ~ pc1 + pc2, data = g)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.122 -3.155 1.295 4.938 10.348
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 92.3746 0.6026 153.288 <2e-16 ***
## pc1 0.1256 0.2147 0.585 0.5599
## pc2 -0.7165 0.3468 -2.066 0.0411 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.49 on 113 degrees of freedom
## Multiple R-squared: 0.0392, Adjusted R-squared: 0.0222
## F-statistic: 2.305 on 2 and 113 DF, p-value: 0.1044
## df AIC
## weight_lm 6 721.1667
## weight_lm_exp_only 4 768.0702
### Prepare the annotation data frame for the heatmap
annotation_df <- g %>%
dplyr::select(c("EH_ID", "Parasite_challenge", "infection_history"))
### Data tidying for the heatmap function
gene_imp <- g %>% left_join(imputed_gene, by = c("pc1", "pc2"))
#remove all columns of the non-imputed data
gene_imp = gene_imp[,!grepl(".x$",names(gene_imp))]
#remove the suffix y
gene_imp <- gene_imp %>% rename_with(~str_remove(., '.y'))
gene <- gene_imp %>% dplyr::select(c("EH_ID", "CXCR3_bio", "IL.6",
"IL.10", "IL.13", "IL.10", "IL.13", "IL1RN", "CASP1", "CXCL9",
"IDO1", "IRGM1", "MPO", "MUC2", "MUC5AC", "MYD88",
"NCR1", "PRF1", "RETNLB", "SOCS1", "TICAM1", "TNF"))
# turn the data frame into a matrix and transpose it. We want to have each cell
# type as a row name
gene <- t(as.matrix(gene))
#switch the matrix back to a data frame format
gene <- as.data.frame(gene)
# turn the first row into column names
gene %>%
row_to_names(row_number = 1) -> gene
# Now further prepare the data frame for plotting by removing the first row
## and convert the column to row names with the cells
gene[-1, ] -> heatmap_data
table(rowSums(is.na(heatmap_data)) == nrow(heatmap_data))
##
## FALSE
## 18
# turn the columns to numeric other wise the heatmap function will not work
heatmap_data[] <- lapply(heatmap_data, function(x) as.numeric(as.character(x)))
# remove columns with only NAs
heatmap_data <- Filter(function(x)!all(is.na(x)), heatmap_data)
#remove rows with only Nas
heatmap_data <- heatmap_data[, colSums(is.na(heatmap_data)) != nrow(heatmap_data)]
rownames(annotation_df) <- colnames(heatmap_data)
Heatmap on gene expression data:
################################### FACS #######################################
all_of(CellCount.cols) instead of
CellCount.cols to silence this message.
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-33-1.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-34-1.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-35-1.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-36-1.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-37-1.png" width="672" />
###### PCA FACS ###################################################################
infection
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-39-1.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-40-1.png" width="672" />
stat_bin() using bins = 30. Pick better
value with binwidth.
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-41-1.png" width="672" />
stat_bin() using bins = 30. Pick better
value with binwidth.
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-41-2.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-43-1.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-44-1.png" width="672" /><img src="Gene_expression_total_files/figure-html/unnamed-chunk-44-2.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-45-1.png" width="672" /><img src="Gene_expression_total_files/figure-html/unnamed-chunk-45-2.png" width="672" />
We will now continue by using an iterative pca to impute missing data
A. Initialization: impute using the mean
B. Step lampda:
# a. do pca on imputed data table S dimensions retained
# b. missing data imputed using pca
# c. means (and standard deviations) updated
C. Iterate the estimation and imputation steps (until convergence)
(convergence: the act of converging and especially moving toward union or uniformity)
Overfitting is a common problem due to believing too much in links between variables.
--> regularized iterative PCA (This version is what is being implented in missMDA)
This is a way of taking less risk when imputing the missing data.
The algorithm estimates the missing data values with values that have no influence
on the PCA results, i.e., no influence on the coordinates of the individals or variables.
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-46-1.png" width="672" /><img src="Gene_expression_total_files/figure-html/unnamed-chunk-46-2.png" width="672" />
Caution: When imputing data, the percentages of inertia associated with the first dimensions will be overestimated.
Another problem: the imputed data are, when the pca is performed considered like real observations.
But they are estimations!!
Visualizing uncertainty due to issing data:
--> mulrimple imputation: generate several plausible values for each missing data point
We here visualize the variability, that is uncertainty on the plane defined by two pca axes.
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-48-1.png" width="672" /><img src="Gene_expression_total_files/figure-html/unnamed-chunk-48-2.png" width="672" /><img src="Gene_expression_total_files/figure-html/unnamed-chunk-48-3.png" width="672" /><img src="Gene_expression_total_files/figure-html/unnamed-chunk-48-4.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-48-5.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-48-6.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-48-7.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-48-8.png" width="672" />
Individuals lying on the axis have no missing data, but individuals that far away have many missing data.
big ellipse = big uncertainty
tight elipse (line) = low uncertainty
Variable representation:
Poins tight together )look like one) - have no missing variables --> low uncertainty
Points spread -- > higher variability -- > higher uncertainty
High uncertainty--> we should interpret the result with care
The individuals with many missing data values make the axes move,
and thus the positions of all individuals
Therefore in the last plots every individual is getting an eclipse as they are as well influenced by the missing data of the others.
THe plot with the dimensions shows the projections of the pca dimensions of each imputed table on the pca plane obtained using the original imputed data table
As all of the arrows are close to either the first or second axes,
this means that the axes are stable with respect to the set of imputed tables --> we don't have evidence of instability here.
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-50-1.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-51-1.png" width="672" />
The function fviz_contrib() [factoextra package] can be used to draw a bar plot of variable contributions. If your data contains many variables, you can decide to show only the top contributing variables. The R code below shows the top 10 variables contributing to the principal components:
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-52-1.png" width="672" /><img src="Gene_expression_total_files/figure-html/unnamed-chunk-52-2.png" width="672" />
The total contribution to PC1 and PC2 is obtained with the following R code:
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-53-1.png" width="672" />
The red dashed line on the graph above indicates the expected average contribution. If the contribution of the variables were uniform, the expected value would be 1/length(variables) = 1/10 = 10%. For a given component, a variable with a contribution larger than this cutoff could be considered as important in contributing to the component.
Note that, the total contribution of a given variable, on explaining the variations retained by two principal components, say PC1 and PC2, is calculated as contrib = [(C1 * Eig1) + (C2 * Eig2)]/(Eig1 + Eig2), where
C1 and C2 are the contributions of the variable on PC1 and PC2, respectively
Eig1 and Eig2 are the eigenvalues of PC1 and PC2, respectively. Recall that eigenvalues measure the amount of variation retained by each PC.
In this case, the expected average contribution (cutoff) is calculated as follow: As mentioned above, if the contributions of the 10 variables were uniform, the expected average contribution on a given PC would be 1/10 = 10%. The expected average contribution of a variable for PC1 and PC2 is : [(10* Eig1) + (10 * Eig2)]/(Eig1 + Eig2)
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-54-1.png" width="672" />
To visualize the contribution of individuals to the first two principal components, type this:
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-55-1.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-56-1.png" width="672" /><img src="Gene_expression_total_files/figure-html/unnamed-chunk-56-2.png" width="672" />
PCA + Biplot combination
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-57-1.png" width="672" />
In the following example, we want to color both individuals and variables by groups. The trick is to use pointshape = 21 for individual points. This particular point shape can be filled by a color using the argument fill.ind. The border line color of individual points is set to “black” using col.ind. To color variable by groups, the argument col.var will be used.
To customize individuals and variable colors, we use the helper functions fill_palette() and color_palette() [in ggpubr package].
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-58-1.png" width="672" />
<img src="Gene_expression_total_files/figure-html/unnamed-chunk-59-1.png" width="672" />
################## FACS - Genes Imputation and pca ############################
# 1. Start by combining the data sets
```r
## Adding prefixes to the columns of each data frame and joining
#Adding the suffix G to the genes
colnames(gene_expr) <- paste("G_", colnames(gene_expr), sep = "")
gene_expr <- gene_expr %>% rename(EH_ID = G_EH_ID,
primary_infection = G_primary_infection,
challenge_infection = G_challenge_infection,
infection_history = G_infection_history,
mouse_strain = G_mouse_strain,
max_WL = G_max_WL,
delta = G_delta,
Parasite_challenge = G_Parasite_challenge)
#Adding the suffix f to the facs data
colnames(facs_data) <- paste("F_", colnames(facs_data), sep = "")
facs_data <- facs_data %>% rename(EH_ID = F_EH_ID,
primary_infection = F_primary_infection,
challenge_infection = F_challenge_infection,
infection_history = F_infection_history,
mouse_strain = F_mouse_strain,
max_WL = F_max_WL,
Parasite_challenge = F_Parasite_challenge)
immune_data <- gene_expr %>% full_join(facs_data, by = intersect(colnames(gene_expr), colnames(facs_data)))
immune_data <- unique(immune_data)
## Warning in PCA(immune): Missing values are imputed by the mean of the variable:
## you should use the imputePCA function of the missMDA package
#let's do a pca while removing ALL NA values
res.NA.remove <- PCA(immune %>% na.omit())
# These are rather unsophisticated ways to solve the problem
We will now continue by using an iterative pca to impute missing data A. Initialization: impute using the mean B. Step lampda: # a. do pca on imputed data table S dimensions retained # b. missing data imputed using pca # c. means (and standard deviations) updated C. Iterate the estimation and imputation steps (until convergence) (convergence: the act of converging and especially moving toward union or uniformity)
Overfitting is a common problem due to believing too much in links between variables. –> regularized iterative PCA (This version is what is being implented in missMDA) This is a way of taking less risk when imputing the missing data. The algorithm estimates the missing data values with values that have no influence on the PCA results, i.e., no influence on the coordinates of the individals or variables.
## G_CXCR3_bio G_IL.6 G_IL.10 G_IL.13 G_IL1RN G_CASP1 G_CXCL9 G_IDO1
## 1 20.92666 21.09045 21.78837 18.65127 16.42338 22.02920 13.60226 13.68551
## 22 21.62075 25.32600 22.92255 19.07832 20.13510 24.25054 14.53048 12.34782
## 43 23.66537 24.18021 24.90025 20.97901 18.14916 22.55511 18.99093 15.90241
## 64 20.21312 23.90781 22.31029 17.45659 16.79377 27.50341 14.03929 12.78334
## 85 23.02829 23.19571 27.67319 20.85165 18.98532 25.45624 19.20542 18.25427
## 106 23.18574 22.59572 25.82543 21.77400 19.45825 23.14097 19.07817 18.48888
## G_IRGM1 G_MPO G_MUC2 G_MUC5AC G_MYD88 G_NCR1 G_PRF1 G_RETNLB
## 1 11.625516 23.16109 11.394231 12.36831 16.85699 23.33234 27.53290 11.389996
## 22 10.033986 26.67972 9.724516 14.59914 18.01044 22.89312 26.26383 7.857130
## 43 7.810604 23.03681 7.749293 12.87121 20.05994 23.96486 26.67386 9.184355
## 64 10.157602 27.67628 7.183272 14.04150 15.61895 23.45405 23.24062 3.920192
## 85 9.241544 22.25922 9.869590 14.37152 17.53845 24.12714 27.09015 8.711133
## 106 9.197374 24.94612 8.225922 11.58353 20.05389 25.43377 27.84301 15.803676
## G_SOCS1 G_TICAM1 G_TNF F_CD4 F_Treg F_Div_Treg F_Treg17 F_Th1
## 1 13.025961 19.82281 21.01065 44.900 6.385 16.205 13.520 6.780
## 22 10.292493 17.66099 22.36282 46.145 7.005 21.365 11.565 10.920
## 43 9.205008 19.11736 22.81213 56.220 7.150 12.455 9.505 2.965
## 64 10.692568 15.46167 18.96024 40.590 6.450 23.760 12.780 9.250
## 85 10.586118 17.03506 24.77639 52.245 8.695 13.465 14.400 2.545
## 106 10.037031 18.92915 25.01909 46.895 6.890 13.355 7.035 2.900
## F_Div_Th1 F_Th17 F_Div_Th17 F_CD8 F_Act_CD8 F_Div_Act_CD8 F_IFNy_CD4
## 1 71.200 0.890 46.875 14.390 11.500 49.520 4.915
## 22 75.115 1.075 42.390 13.840 13.205 59.090 9.085
## 43 19.840 1.630 30.055 10.020 10.915 11.535 3.045
## 64 81.210 1.705 78.305 25.305 11.105 55.935 9.085
## 85 27.850 1.060 27.445 17.550 9.815 12.830 2.005
## 106 25.520 0.695 32.195 7.490 5.395 21.310 2.795
## F_IFNy_CD8
## 1 21.740
## 22 27.535
## 43 41.360
## 64 38.165
## 85 19.390
## 106 19.230
## $Dim.1
## $quanti
## correlation p.value
## F_Th1 0.7650588 1.703309e-24
## F_Th17 0.7598164 5.340582e-24
## F_IFNy_CD8 0.7407478 2.697419e-22
## F_IFNy_CD4 0.7316087 1.568174e-21
## G_IL.13 0.7122022 5.241535e-20
## G_IL1RN 0.7084149 1.005338e-19
## G_IDO1 0.6947200 9.739906e-19
## G_TNF 0.6888737 2.471676e-18
## F_Div_Th17 0.6506015 6.644992e-16
## G_MPO 0.6252548 1.773772e-14
## G_RETNLB 0.5982680 4.280621e-13
## F_Act_CD8 0.5668512 1.220574e-11
## F_Treg 0.5515657 5.504312e-11
## G_IL.10 0.5408752 1.509767e-10
## F_Div_Th1 0.5257661 5.923963e-10
## G_CXCR3_bio 0.4899884 1.168833e-08
## G_MYD88 0.4702646 5.255444e-08
## G_TICAM1 0.4701173 5.312920e-08
## G_PRF1 0.4668096 6.773196e-08
## F_Div_Treg 0.4444984 3.264315e-07
## F_Div_Act_CD8 0.4312808 7.871126e-07
## G_IL.6 0.4176539 1.877346e-06
## G_NCR1 0.4097123 3.062324e-06
## G_MUC5AC 0.3929269 8.273247e-06
## G_CXCL9 0.3664398 3.569232e-05
## G_CASP1 0.3418565 1.242051e-04
## F_Treg17 0.2465892 6.399767e-03
## G_IRGM1 -0.5211005 8.914897e-10
## G_SOCS1 -0.5833882 2.188131e-12
## F_CD8 -0.6968069 6.947760e-19
## F_CD4 -0.8437915 5.900136e-34
##
## attr(,"class")
## [1] "condes" "list"
##
## $Dim.2
## $quanti
## correlation p.value
## G_CXCL9 0.7283817 2.870119e-21
## G_IL.13 0.6706403 3.939175e-17
## G_IL.10 0.6441883 1.570495e-15
## G_PRF1 0.6185593 4.020897e-14
## G_TICAM1 0.6112244 9.640520e-14
## G_NCR1 0.6098601 1.131526e-13
## G_TNF 0.5964205 5.265852e-13
## G_RETNLB 0.5650170 1.468355e-11
## G_IDO1 0.5014129 4.680602e-09
## G_CXCR3_bio 0.4718764 4.664334e-08
## G_MYD88 0.4597753 1.125655e-07
## G_IL.6 0.4491703 2.370129e-07
## G_IRGM1 0.4219901 1.429567e-06
## F_CD4 0.3055332 6.547726e-04
## G_SOCS1 0.2532034 5.076460e-03
## F_Treg -0.2380665 8.551869e-03
## F_IFNy_CD8 -0.2575118 4.351615e-03
## F_CD8 -0.3127221 4.789682e-04
## G_MPO -0.3673520 3.401058e-05
## F_IFNy_CD4 -0.3945495 7.533015e-06
## F_Th1 -0.5348894 2.615960e-10
## F_Div_Th17 -0.5654332 1.408179e-11
## F_Act_CD8 -0.6210470 2.973398e-14
## F_Div_Treg -0.6398160 2.790472e-15
## F_Div_Act_CD8 -0.7326830 1.279869e-21
## F_Div_Th1 -0.7673426 1.025732e-24
##
## attr(,"class")
## [1] "condes" "list"
##
## $Dim.3
## $quanti
## correlation p.value
## G_MUC2 0.7709011 4.600148e-25
## G_CASP1 0.7312700 1.671562e-21
## G_MUC5AC 0.6001274 3.470433e-13
## G_SOCS1 0.5513289 5.630884e-11
## G_IRGM1 0.4754587 3.569935e-08
## G_CXCR3_bio 0.3000311 8.274102e-04
## G_MYD88 0.2150116 1.786775e-02
## G_MPO 0.1995167 2.823459e-02
## G_CXCL9 -0.2240811 1.348067e-02
## G_TICAM1 -0.2308450 1.085158e-02
##
## attr(,"class")
## [1] "condes" "list"
##
## $call
## $call$num.var
## [1] 1
##
## $call$proba
## [1] 0.05
##
## $call$weights
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [112] 1 1 1 1 1 1 1 1 1 1
##
## $call$X
## Dim.1 G_CXCR3_bio G_IL.6 G_IL.10 G_IL.13 G_IL1RN G_CASP1
## 1 0.38393739 20.92666 21.09045 21.78837 18.65127 16.42338 22.02920
## 22 2.63643667 21.62075 25.32600 22.92255 19.07832 20.13510 24.25054
## 43 2.00034162 23.66537 24.18021 24.90025 20.97901 18.14916 22.55511
## 64 2.01438301 20.21312 23.90781 22.31029 17.45659 16.79377 27.50341
## 85 1.26179437 23.02829 23.19571 27.67319 20.85165 18.98532 25.45624
## 106 2.06168075 23.18574 22.59572 25.82543 21.77400 19.45825 23.14097
## 127 2.38696055 20.19632 23.91450 21.62915 18.76407 18.55582 23.11127
## 148 2.78216918 23.73105 21.14346 23.61026 19.84489 17.67666 25.06357
## 169 4.50400857 23.18462 22.02135 24.37189 20.88345 19.31653 22.45011
## 190 -0.27703529 19.21698 19.62519 22.94861 16.18605 17.29027 23.55407
## 211 0.87599108 22.52077 23.65471 23.85751 20.73572 20.58918 23.81598
## 232 0.44771425 19.12177 25.26331 20.62422 16.14895 17.38254 22.70095
## 253 -0.70630212 22.45032 22.69335 23.61657 19.44235 17.74972 22.49518
## 274 0.20902462 22.51152 20.95665 23.01596 18.99110 16.69397 22.84267
## 295 -0.30595182 21.26747 21.85538 23.74287 19.62806 19.67336 22.04784
## 316 -3.29612066 18.00746 18.38914 18.74826 16.15896 15.10803 23.38067
## 337 1.92481446 19.10121 20.98553 22.42743 17.74906 16.44270 23.42149
## 358 0.89430406 22.41295 20.25383 23.03015 20.86906 17.63167 22.85872
## 379 -0.02297122 21.44775 18.45020 27.89777 18.26056 17.32784 23.05298
## 400 -0.90422295 21.07130 20.03526 21.08242 16.86255 17.43922 22.51961
## 421 0.54713244 20.92691 21.09167 24.07971 18.20536 17.14403 22.76425
## 442 -2.97562943 19.36417 15.07182 20.66591 16.07438 16.54046 24.16598
## 463 0.27535175 18.14328 17.39709 21.31080 15.86963 12.63218 23.57993
## 484 -0.14036040 20.03795 28.89199 21.07542 18.05607 18.66006 22.98125
## 505 -0.42429273 23.44335 23.78059 24.23830 20.46744 16.75777 23.76993
## 526 -0.71666176 20.31368 19.93494 21.62254 16.87035 17.64324 22.86814
## 547 0.86995217 24.81556 21.68421 25.12770 21.64005 18.20610 22.86023
## 568 -1.58024050 20.53629 25.89126 23.68561 19.78150 16.66748 28.45142
## 589 1.40301639 20.53802 20.02823 20.76649 18.60375 17.42489 22.69451
## 610 -1.32821772 18.97607 19.07150 21.15728 15.69609 13.40232 24.16373
## 631 0.04307676 23.27692 19.71861 23.52992 19.80666 19.58139 21.79801
## 652 -0.89863421 21.66393 20.33407 20.44784 19.45649 17.72250 23.41526
## 673 0.26367230 23.07634 22.39279 23.69841 19.64607 19.91583 23.28426
## 694 0.89455474 22.53733 18.60527 22.20044 18.56122 17.97018 25.19149
## 715 1.36682346 22.10287 20.06929 23.90926 20.00712 19.46909 21.63034
## 736 -0.39813847 24.60278 18.46774 26.19512 19.99267 19.76563 23.74273
## 757 -4.48215599 18.58505 19.05836 17.86940 15.96475 14.97143 20.93711
## 778 -1.35581435 16.86408 13.21835 17.79117 13.30510 14.25306 24.43256
## 799 0.74871763 22.15447 25.41724 22.04275 18.07179 17.18358 29.98603
## 820 -0.53626902 21.16552 18.10097 22.65766 18.78266 17.71976 24.28977
## 841 -1.09130055 24.69742 19.05980 23.16757 19.00740 18.98606 22.78772
## 862 0.33945821 21.32868 21.65526 23.07222 18.96714 17.83004 22.53197
## 883 -3.10404161 18.70600 17.79219 18.49236 14.44634 14.68719 24.20202
## 904 -1.26449650 22.12217 21.87536 23.32834 19.35099 18.26465 23.79661
## 925 -2.08908093 19.16785 17.97426 19.89393 14.76001 15.60916 23.59150
## 946 -3.96131425 18.19756 14.40759 20.83681 15.31739 17.24873 25.16027
## 967 -2.21909310 21.64540 17.73381 20.98086 17.60556 17.40872 20.43007
## 988 -1.42807826 20.18662 16.57967 19.05747 16.36073 16.32045 22.82450
## 989 -1.46939246 18.21390 29.81903 18.33959 15.01577 13.28305 25.93133
## 1010 -2.10884520 20.61515 23.03621 29.98877 20.24780 12.75221 20.43024
## 1011 -0.95106875 21.00294 23.67766 24.20689 20.77857 15.08824 20.90917
## 1012 -4.37971101 20.65725 21.54047 23.25961 18.17757 11.65156 22.92319
## 1013 -0.89023691 21.31698 26.71171 25.52867 21.11842 13.83283 21.43852
## 1014 -4.73594992 20.20715 24.37765 22.34004 18.79052 11.97324 21.03117
## 1015 -4.27283734 18.40655 21.07280 21.44767 16.18907 11.82725 21.70017
## 1016 -3.29612865 20.89049 23.48067 22.36207 18.97398 11.85427 21.44578
## 1017 -2.44217906 21.14188 22.70663 23.60720 19.39390 13.10425 25.34167
## 1018 0.77833863 21.95768 22.34438 26.11948 20.66828 15.37061 21.28205
## 1019 -4.36799169 18.21933 25.24031 20.51353 16.96765 12.28923 22.26009
## 1020 -3.27490287 24.65157 23.53264 23.43752 19.89853 11.43627 25.73564
## 1021 -2.73705403 23.52242 27.13311 24.22711 19.87466 11.27634 21.92730
## 1022 7.72587673 22.91576 25.39795 28.87344 24.53315 16.75650 22.16068
## 1043 8.32409310 25.66519 26.35204 27.17831 24.41435 19.70521 26.08998
## 1064 6.99688301 24.22064 26.80839 28.05381 24.85629 19.23186 27.75083
## 1085 2.79282594 22.86653 23.56129 25.01750 22.76053 18.03112 21.69953
## 1106 6.21696744 22.76071 25.75475 27.95595 23.56784 15.84708 23.58463
## 1127 8.68538312 23.52785 29.95433 28.18004 25.14229 23.13962 24.40739
## 1148 7.73408669 22.75096 26.15021 25.69999 24.13682 17.58811 23.01611
## 1169 3.54490029 21.48844 22.60560 29.13131 22.81402 18.63039 20.75492
## 1190 8.92920843 25.80037 29.77186 29.09962 26.19730 20.02498 26.91510
## 1211 3.03849241 21.03955 26.23716 26.44454 21.78755 16.61041 22.30920
## 1232 6.58125165 21.52073 27.46334 24.91564 22.51335 17.10527 24.02626
## 1253 6.57389787 22.66652 18.92939 25.56209 22.48327 18.86001 24.83386
## 1274 -3.01546346 21.81679 20.56615 26.30993 18.96533 12.25711 21.65407
## 1275 4.31479824 22.67323 26.18491 27.22396 24.69858 20.08638 25.34344
## 1296 2.34693984 23.46890 22.68031 23.16663 22.41758 18.06204 22.36512
## 1297 -4.55987557 19.91255 22.64689 22.62087 17.89643 11.27495 21.54675
## 1298 -4.39196613 20.08603 21.31040 22.15091 17.60702 10.39335 20.70334
## 1299 8.47098790 24.06576 28.75247 23.54490 22.87320 21.42000 27.75544
## 1300 -3.67765924 21.27995 18.29274 24.38039 18.24103 12.06338 20.29093
## 1301 -4.27505546 20.22281 24.09667 19.95704 17.03426 12.45559 21.84692
## 1302 -3.80723774 24.54876 24.16064 25.98836 21.00168 14.72332 24.56166
## 1303 -3.08238850 19.66524 28.21305 25.28405 20.88149 12.24016 21.28489
## 1304 -1.16370423 21.37939 22.23118 24.59390 20.27709 17.24273 21.67512
## 1305 -2.59057394 20.76001 22.04766 22.25595 17.90817 15.60735 20.92126
## 1306 -2.88781460 18.55728 25.20569 24.22079 18.44548 15.59951 19.99790
## 1307 5.08656521 20.76581 23.12287 24.20175 24.65534 16.35892 21.11699
## 1308 -3.78660664 19.80003 22.51022 24.68163 18.29073 12.63565 23.09224
## 1309 -3.90317899 20.95861 22.68883 26.12950 20.04791 11.69210 22.80543
## 1310 -3.94140571 21.59717 26.58406 21.70019 21.35713 11.07716 20.93479
## 1311 -3.83609061 18.34869 21.28534 21.67449 15.43664 14.73684 19.96002
## 1312 -1.73286023 21.69704 25.01886 23.22688 17.92247 15.92684 21.19813
## 1313 0.33646080 21.45424 19.31163 23.59355 18.98706 18.17187 22.41502
## 1314 -5.47990797 19.13856 16.59937 17.90145 14.23954 12.16899 21.02919
## 1315 0.88873573 20.68170 26.84019 24.26723 19.69519 17.50911 20.48537
## 1334 -0.62043459 18.54700 23.16907 23.37539 20.64206 17.68361 21.37431
## 1353 0.81885489 20.46746 18.96176 24.76140 17.74507 17.02771 20.42448
## 1372 0.87465675 19.20522 21.60006 22.75786 19.52374 19.51251 20.75696
## 1391 -4.02784785 21.53098 18.24249 22.16032 17.34487 13.69251 24.61451
## 1392 2.03632707 20.54109 26.92355 21.56791 22.61048 20.05260 24.82729
## 1411 -0.78981833 20.32615 23.60529 21.83610 16.52889 15.60828 20.62177
## 1430 -0.58085630 20.58743 22.64934 21.05282 15.64012 15.78011 21.04427
## 1449 -0.52696669 21.30977 24.81393 20.53981 15.96387 15.62994 22.11439
## 1468 1.78942024 24.78347 20.20337 23.52439 19.78487 14.97696 22.93029
## 1487 3.50023687 22.77867 25.05195 25.39121 23.10120 20.21300 25.57550
## 1506 -1.17400431 20.05828 17.73281 19.67574 14.96183 14.91150 20.39827
## 1525 0.06090527 20.06144 19.48198 22.33842 15.84020 15.91221 20.98834
## 1544 -4.80499397 21.33039 19.22344 21.16372 16.83008 12.50428 22.24713
## 1545 -0.83680192 21.08006 18.49392 19.74151 15.73607 12.83904 21.46682
## 1564 0.65298618 18.95654 21.82732 26.77299 21.41995 19.69194 20.78469
## 1583 1.32430798 20.24860 28.76398 23.93211 21.10862 20.95269 21.23007
## 1602 -0.24747765 19.01495 26.92797 23.32124 20.67509 18.21358 20.67898
## 1621 0.39545401 22.14929 22.09470 24.41267 16.81424 17.08754 20.84055
## 1640 -4.62314088 23.41073 17.46569 19.79551 14.49658 13.13472 25.08039
## 1641 -0.32658386 18.84797 25.09494 24.87735 20.31023 15.62935 20.16156
## 1660 0.86829918 21.05519 27.11805 23.21401 20.25871 18.40590 21.07134
## 1679 3.09061869 21.52990 22.73974 23.55340 19.81853 18.21812 23.60838
## 1700 1.98977099 21.62663 22.96523 23.84156 20.00586 17.53337 23.29520
## 1721 -0.97944106 19.21490 18.83110 19.56207 14.95676 16.12013 23.15203
## 1742 -2.35460526 20.56672 21.29702 22.25107 17.74903 15.06501 22.43768
## 1763 0.55363583 20.87223 21.69687 22.55136 18.42015 16.78295 23.11778
## G_CXCL9 G_IDO1 G_IRGM1 G_MPO G_MUC2 G_MUC5AC G_MYD88
## 1 13.60226 13.685507 11.625516 23.16109 11.394231 12.368312 16.856985
## 22 14.53048 12.347823 10.033986 26.67972 9.724516 14.599135 18.010443
## 43 18.99093 15.902410 7.810604 23.03681 7.749293 12.871210 20.059938
## 64 14.03929 12.783337 10.157602 27.67628 7.183272 14.041496 15.618948
## 85 19.20542 18.254268 9.241544 22.25922 9.869590 14.371520 17.538455
## 106 19.07817 18.488880 9.197374 24.94612 8.225922 11.583533 20.053889
## 127 14.67773 14.430931 8.600942 24.90775 8.730690 11.900492 18.177256
## 148 14.21946 15.666291 8.297135 25.61896 7.522414 13.148207 19.038180
## 169 16.20309 14.952342 8.997360 29.21133 8.156661 8.684992 20.392755
## 190 12.88829 11.663551 9.052160 27.46451 8.642571 10.342714 14.618691
## 211 20.30617 16.930006 8.162201 25.54124 8.859693 15.460500 19.281729
## 232 13.01806 10.705361 7.565302 24.91439 6.904949 15.359870 14.612337
## 253 17.39209 15.675249 9.841508 25.19862 7.871219 8.678551 16.285136
## 274 15.54217 13.079090 10.548003 23.12428 9.808142 10.449504 16.981842
## 295 19.29231 18.558979 9.218357 28.14862 8.669347 10.198480 16.960683
## 316 17.12064 15.731242 9.193427 23.38627 8.394537 10.196126 14.609839
## 337 13.68531 12.914861 9.322633 21.87048 8.714876 12.295662 15.888646
## 358 18.63569 19.069602 9.447187 27.92150 8.040773 9.121950 17.378285
## 379 12.95849 14.508282 9.598510 27.07087 7.807939 10.415893 15.854892
## 400 14.61636 13.138920 8.335187 24.66545 7.790361 9.038129 16.616529
## 421 16.18053 13.646650 9.565223 25.42206 8.771323 9.468288 15.065539
## 442 15.03703 16.004009 8.438642 27.97673 8.473955 10.951688 12.671592
## 463 14.00879 11.186614 9.439790 25.15912 8.613752 20.293679 13.916375
## 484 14.61884 12.098614 8.954314 24.31267 17.990707 24.237810 15.120134
## 505 21.33524 18.017771 11.480787 19.99031 10.255215 10.923709 17.310957
## 526 16.94201 12.246575 8.748695 26.20443 7.940369 12.292991 15.518893
## 547 18.99404 18.253549 10.577026 21.14607 8.761090 9.023115 19.547397
## 568 16.56531 16.273956 13.691213 19.74174 12.038068 20.929919 15.678849
## 589 15.85200 12.968113 8.203141 24.26771 8.233775 17.425917 17.354687
## 610 13.93241 11.229936 9.725386 24.64733 6.814177 11.003653 13.408224
## 631 18.71677 17.629490 10.881357 25.72409 10.267396 11.219287 15.989496
## 652 19.96504 19.114217 11.739965 21.94526 12.198908 12.960735 16.747558
## 673 18.19233 16.734890 8.942380 24.38990 8.418066 9.847442 16.538393
## 694 18.54367 17.279974 9.036738 22.05586 7.435172 13.026381 16.057834
## 715 17.56039 18.416046 8.848435 25.72081 8.204233 9.882749 18.079438
## 736 18.40169 19.753084 9.752966 28.66910 9.577180 10.404196 17.139011
## 757 16.51682 16.471883 11.495214 20.75777 10.413618 11.989536 14.774482
## 778 13.82651 8.661838 7.154126 23.86028 7.951477 15.116064 10.230339
## 799 13.24525 13.915862 8.987010 27.49619 9.597302 21.741745 16.270490
## 820 17.31654 17.871126 10.481867 23.27109 9.326657 9.908069 15.881726
## 841 18.82635 17.110750 10.481346 24.32100 8.573053 9.253118 16.642453
## 862 17.26648 15.929076 8.958850 22.70039 7.632720 8.440455 19.807910
## 883 12.21244 9.754557 9.836893 23.37686 9.851718 11.585622 14.407068
## 904 20.24753 19.708596 9.977461 24.92838 8.415812 8.076470 17.337172
## 925 13.56512 9.842353 9.029007 24.40325 9.316026 9.889951 13.850419
## 946 16.38290 15.927925 8.049613 20.55254 7.563250 12.350998 11.128010
## 967 16.55790 15.251946 9.385581 27.61566 8.563067 9.972695 15.725963
## 988 17.97308 18.265865 9.486106 23.34994 7.878306 10.787435 12.493822
## 989 11.98283 10.025161 8.136754 27.16886 10.834516 29.918079 13.929742
## 1010 18.32872 16.717158 10.030781 16.37685 8.541946 8.852514 20.404963
## 1011 21.96734 18.171699 9.531294 15.92918 7.957801 8.211709 24.785884
## 1012 16.90758 12.292333 11.168791 17.07884 8.345124 10.313463 15.319679
## 1013 22.16466 18.373123 9.563630 16.38449 8.132526 8.572920 23.240718
## 1014 16.66383 11.993194 11.576390 17.15236 10.280913 10.532018 18.139879
## 1015 15.42738 12.523361 9.928879 16.55492 8.291121 9.120236 13.839477
## 1016 16.72246 13.721075 10.479662 16.32184 8.641474 8.817069 19.929199
## 1017 18.64811 15.843818 10.788702 17.07038 9.428260 9.364003 18.078884
## 1018 22.49707 18.930756 8.050492 16.71614 7.611355 7.888725 20.995390
## 1019 15.25164 11.803676 10.108555 16.57170 9.364101 9.848285 15.544608
## 1020 20.65578 12.237259 11.398526 16.60661 9.628627 9.639826 19.190942
## 1021 18.51135 13.708155 10.256888 16.39160 9.063478 9.058345 20.478204
## 1022 23.45426 21.459525 7.149357 25.63594 6.211322 10.154484 24.906656
## 1043 19.96006 20.724537 9.016223 27.77559 9.246984 14.123916 24.948713
## 1064 23.07473 27.169505 8.986193 27.97227 8.883982 23.694956 27.782637
## 1085 24.18800 22.517576 8.747040 26.39468 7.865111 9.540464 19.913584
## 1106 23.33492 22.130637 9.505613 20.34651 9.117813 10.210623 25.644537
## 1127 22.51919 24.362430 7.028294 27.61117 9.249620 25.681823 23.705403
## 1148 24.12845 22.364820 7.679259 28.01318 7.529806 12.495365 24.056632
## 1169 22.14808 21.229097 8.823074 23.37908 7.071763 8.979468 18.841489
## 1190 23.73669 26.746953 10.566932 27.03879 10.301982 15.246147 24.071985
## 1211 20.71644 20.531902 8.015308 26.53156 6.875894 15.616582 18.824360
## 1232 18.86451 21.448918 7.324264 27.47612 6.626930 13.267206 25.219254
## 1253 16.34429 22.097978 7.796770 27.26642 8.052046 18.066238 24.484515
## 1274 13.14677 13.300336 10.259382 16.46249 8.504597 8.874519 20.875416
## 1275 23.74179 25.029717 9.255368 22.75586 8.579815 29.113148 28.078962
## 1296 19.88270 20.563533 10.008556 22.27321 8.371019 9.336553 24.674035
## 1297 18.09229 12.713460 10.729052 16.12279 9.020236 9.326122 17.670409
## 1298 18.47461 11.083212 9.706705 15.60862 8.225850 8.669181 17.396433
## 1299 18.54329 18.841289 7.212158 28.72646 11.580169 26.744894 20.536848
## 1300 14.49042 12.360175 10.292874 16.43850 8.630854 8.630570 17.291781
## 1301 14.45594 11.304476 9.925298 17.66268 9.721816 10.491249 15.854700
## 1302 22.72566 15.063209 14.224817 20.66631 12.365167 12.636119 18.984608
## 1303 23.29208 13.730573 11.186153 16.54841 9.411632 9.773155 28.008621
## 1304 19.01887 18.925460 10.323671 17.42215 8.655927 9.526401 18.953311
## 1305 14.94362 12.729950 9.898791 17.78050 8.541098 8.728032 16.724469
## 1306 18.02023 16.255302 10.261519 17.17013 8.567059 8.840712 17.923550
## 1307 21.25767 21.997595 7.290380 28.70681 6.445662 9.138264 13.951069
## 1308 20.79058 13.061516 11.602668 17.49598 9.719942 10.305993 10.797975
## 1309 21.78558 12.274416 11.183381 17.01788 9.354890 9.778690 10.666151
## 1310 22.47699 11.437480 10.668408 16.28529 8.850896 9.096841 10.200785
## 1311 15.04185 13.407077 9.601861 16.79333 7.966876 8.117302 9.107979
## 1312 18.33013 15.595453 9.425018 16.97132 7.794905 8.401166 9.336994
## 1313 14.38687 12.455074 9.436140 24.79474 8.197041 9.244237 9.956077
## 1314 10.82695 9.136530 9.375088 17.69353 8.866534 9.777502 10.271472
## 1315 18.70781 14.946433 8.839694 19.82217 7.487277 8.125193 8.844189
## 1334 24.86841 19.502043 9.457993 18.28340 8.071410 8.206934 9.252441
## 1353 15.35375 14.252057 9.304423 23.43023 7.997043 9.088218 9.269372
## 1372 18.79592 16.970430 8.739251 20.15552 9.256436 10.444694 10.814310
## 1391 14.09206 12.763815 12.235026 19.78562 11.179115 11.697763 12.527439
## 1392 18.86993 17.037959 10.412347 19.15029 9.342203 9.990472 11.061339
## 1411 13.72277 12.100585 8.635025 19.64736 7.290007 8.052774 8.988102
## 1430 14.14905 14.815813 9.722631 18.87126 8.935368 10.212263 10.256080
## 1449 14.05901 11.611228 8.832139 17.72639 7.722895 8.278575 9.471053
## 1468 16.14029 14.976568 10.745571 18.11004 9.538819 10.048293 10.673092
## 1487 21.90772 20.337306 10.781881 19.84596 9.299197 9.821379 10.803154
## 1506 12.87900 11.674964 8.890484 21.49815 8.237312 8.762589 9.752521
## 1525 11.55303 11.659147 9.496184 20.05410 7.969417 8.572635 9.429172
## 1544 15.30404 11.142649 11.492399 18.39825 10.125236 10.724162 11.321831
## 1545 13.54572 11.447434 10.481360 18.73255 9.916628 10.691091 11.307609
## 1564 25.69238 20.921377 9.314263 19.02520 8.686559 9.464939 10.506455
## 1583 25.34770 20.689122 8.418992 24.76759 7.942093 9.095062 9.772552
## 1602 25.74388 20.553644 8.419839 21.41300 6.748056 7.525599 8.790171
## 1621 15.14489 15.490731 9.344918 21.30055 7.847138 8.507111 9.580745
## 1640 12.26390 8.769283 10.113600 19.62256 10.336654 11.690665 10.798740
## 1641 20.93232 18.051913 9.677846 16.56573 7.916451 8.172702 9.524207
## 1660 17.73318 16.366598 8.701905 20.94546 7.665722 8.340444 9.444841
## 1679 17.30498 17.066943 8.655827 25.28843 8.453515 13.596362 16.840473
## 1700 18.03878 17.066228 9.101223 23.82069 8.607356 12.732305 17.097344
## 1721 12.05817 11.001204 8.676909 24.40806 8.526599 12.552244 10.998672
## 1742 16.64099 13.792882 9.982036 20.48069 8.947085 10.482400 14.447618
## 1763 16.37342 15.067583 9.146649 23.40381 8.644727 12.313631 15.194739
## G_NCR1 G_PRF1 G_RETNLB G_SOCS1 G_TICAM1 G_TNF F_CD4 F_Treg
## 1 23.33234 27.53290 11.389996 13.025961 19.82281 21.01065 44.90000 6.385000
## 22 22.89312 26.26383 7.857130 10.292493 17.66099 22.36282 46.14500 7.005000
## 43 23.96486 26.67386 9.184355 9.205008 19.11736 22.81213 56.22000 7.150000
## 64 23.45405 23.24062 3.920192 10.692568 15.46167 18.96024 40.59000 6.450000
## 85 24.12714 27.09015 8.711133 10.586118 17.03506 24.77639 52.24500 8.695000
## 106 25.43377 27.84301 15.803676 10.037031 18.92915 25.01909 46.89500 6.890000
## 127 23.25482 23.54348 11.930951 10.137282 17.89026 20.40686 49.47000 6.065000
## 148 23.69673 28.00436 10.795116 10.187464 17.98634 21.91510 45.74000 6.520000
## 169 23.81112 26.24627 11.763447 9.833251 20.04689 25.99834 46.33000 6.465000
## 190 21.39968 20.45141 4.079604 11.242170 15.12650 18.21831 43.32500 8.915000
## 211 23.66060 26.62192 12.512554 8.390115 17.00279 24.39284 68.01000 3.630000
## 232 20.06957 21.01384 3.598778 8.892853 14.34632 18.18376 37.43500 9.045000
## 253 24.37670 25.10224 11.645965 10.674034 15.64940 20.93638 53.25000 6.895000
## 274 23.76296 27.17679 12.534258 11.718299 17.56715 20.51972 47.34000 6.465000
## 295 23.89841 24.64252 11.212956 10.034478 16.84957 22.49043 61.52500 5.650000
## 316 18.00615 22.71284 6.937463 10.044808 15.08446 17.05868 51.47500 6.690000
## 337 21.33841 26.20900 5.973854 10.589004 17.65482 19.35511 36.15500 8.875000
## 358 29.49340 25.66098 14.362461 10.790189 18.71333 23.10196 54.57500 5.110000
## 379 23.12706 24.63635 5.662282 10.323638 15.91257 19.63243 58.92000 5.075000
## 400 22.28476 23.09671 6.708141 9.097796 16.83769 19.32845 49.92500 7.915000
## 421 24.36829 25.16968 8.373846 10.727382 15.39051 19.76802 53.24000 5.215000
## 442 18.33988 22.09717 3.437346 10.438836 13.27494 18.82194 49.35000 9.015000
## 463 18.49862 22.59840 4.203089 9.684278 13.27406 22.08087 28.29500 27.230000
## 484 20.80061 24.78750 4.605416 10.017204 15.04402 23.69131 53.27000 6.670000
## 505 25.28210 25.69449 9.644582 12.041930 19.34746 26.10923 54.26500 9.475000
## 526 20.79229 26.11614 6.063100 9.980612 14.75829 18.44981 48.49000 5.220000
## 547 23.63638 27.39362 12.795983 9.838008 22.32244 29.87482 56.78000 4.835000
## 568 22.63025 28.71924 13.919183 15.560557 16.95622 20.43844 67.43000 3.900000
## 589 21.23689 29.16415 9.982388 9.482890 14.86344 21.08135 53.51000 4.525000
## 610 20.03371 21.10798 5.917482 11.194286 13.04953 16.84558 49.93500 6.265000
## 631 20.77055 28.50238 10.511800 11.429176 16.45653 24.00758 42.86000 8.465000
## 652 20.53246 29.53929 10.842803 12.155859 17.76277 21.50840 55.30500 7.315000
## 673 25.24495 25.38933 11.824440 9.660671 15.41369 20.83225 52.10000 5.205000
## 694 21.49756 25.56295 7.036342 8.830993 15.62009 20.40643 48.70500 11.315000
## 715 22.91124 25.93300 12.132540 9.535813 16.56348 22.45497 42.07000 5.530000
## 736 21.85548 26.16469 9.879838 11.097173 16.94929 24.08582 55.00500 4.635000
## 757 19.67674 21.14482 8.466972 12.429422 15.73371 16.46384 55.13500 4.955000
## 778 17.36359 18.08027 3.785109 10.974022 12.41300 13.78664 48.92000 14.300000
## 799 23.07639 24.78306 5.259263 10.307205 14.37050 19.70445 60.70500 3.740000
## 820 19.59789 25.15236 11.495341 11.487913 16.29785 20.60002 49.85000 4.700000
## 841 22.90715 25.42066 7.758496 11.493739 17.45863 22.01304 53.75500 9.235000
## 862 24.18657 29.51591 9.225770 9.632405 17.44476 21.63822 48.38000 6.965000
## 883 19.93898 20.38618 4.346449 11.657992 15.33566 15.86004 46.69500 9.310000
## 904 21.63473 28.11725 9.187486 10.970666 19.30253 21.39020 58.17000 7.095000
## 925 18.81508 21.15985 4.867295 11.106637 15.25927 16.16250 50.80000 9.805000
## 946 17.17266 21.54708 3.690941 10.228503 13.47368 18.09514 57.61500 5.520000
## 967 21.39350 23.41759 8.189116 10.139407 15.24493 17.65270 67.75500 3.245000
## 988 17.79122 25.89262 4.204721 10.569843 12.91764 17.50383 50.89402 7.658338
## 989 18.11990 19.92611 3.577107 10.324091 14.54200 16.01331 48.12500 10.595000
## 1010 25.36659 26.01465 10.749170 11.024760 21.19794 21.01304 62.22072 5.119414
## 1011 26.75319 27.09819 9.755923 10.478270 22.50241 21.56508 58.33307 5.882857
## 1012 24.26265 27.12899 10.841208 12.989070 16.99448 20.03119 67.63015 4.134243
## 1013 27.48604 27.18535 9.478791 10.607035 21.82549 21.98348 58.80046 5.767698
## 1014 26.70705 25.41207 12.030827 13.123553 21.09282 21.07389 70.49765 3.512972
## 1015 20.19892 21.79024 9.145387 10.833533 15.29784 19.01250 62.88455 5.218830
## 1016 25.53460 26.41866 9.278296 11.303618 21.34152 21.31616 64.63679 4.699616
## 1017 26.75811 25.29939 9.923647 11.828319 19.06670 21.78523 61.83057 5.248561
## 1018 23.38357 26.57793 8.262385 8.890513 20.80948 23.70044 50.58155 7.472741
## 1019 22.93460 25.11673 9.047844 11.867247 16.30778 18.36694 64.97428 4.746851
## 1020 23.87387 28.88317 9.635853 12.837053 19.15818 22.89580 66.53513 4.258283
## 1021 26.26590 23.85662 9.703631 11.627023 21.52452 22.65241 64.14684 4.747550
## 1022 27.00035 28.91190 18.572389 8.318661 29.57724 23.13135 14.60000 14.000000
## 1043 26.79737 28.72793 17.913556 10.084373 25.58661 27.70538 17.90000 11.800000
## 1064 25.83862 27.59474 20.897073 9.482244 24.73153 27.59754 27.20000 11.500000
## 1085 29.07498 28.08288 16.332964 9.665532 21.42768 23.91542 52.60000 14.400000
## 1106 26.89351 28.29766 9.493187 11.330597 26.12898 26.67485 28.40000 15.200000
## 1127 27.39339 29.29848 14.714598 8.041715 24.10520 28.93255 20.30000 11.100000
## 1148 25.88560 25.43324 20.720319 7.087203 26.26861 27.69078 25.40000 12.000000
## 1169 26.76586 28.02451 10.975465 9.162248 19.60484 29.13404 31.50000 17.500000
## 1190 28.30976 30.16407 22.021335 13.581984 25.90294 28.37664 14.70000 18.900000
## 1211 24.66802 26.78273 13.342864 8.919463 19.84097 25.19713 37.70000 7.470000
## 1232 25.39097 26.69613 20.083060 7.158283 23.30618 28.17372 25.30000 7.830000
## 1253 24.82501 28.62742 22.004654 8.871887 23.74250 28.31769 28.30000 16.700000
## 1274 24.39808 26.19344 9.526062 11.755902 21.52548 20.79691 63.39871 4.953034
## 1275 27.33835 28.89657 18.031914 9.895583 25.98677 27.80121 45.40000 16.100000
## 1296 25.71248 29.79103 15.178442 10.393341 22.46358 27.50077 47.53241 7.994329
## 1297 22.21427 25.55363 9.661429 12.013956 18.22035 19.84642 67.80764 4.114265
## 1298 22.32535 24.21456 8.805372 11.222371 20.81727 19.51511 66.45499 4.407345
## 1299 28.81700 27.39392 16.855267 8.065261 20.60755 23.72752 21.90510 13.203145
## 1300 24.59491 26.21215 9.441200 11.032251 20.47256 20.23849 64.71646 4.725783
## 1301 22.79706 23.15837 9.722345 12.451737 20.65242 17.12110 64.71388 4.796189
## 1302 25.96324 26.79236 13.220426 14.919748 20.57782 22.50920 71.22315 3.236726
## 1303 26.55833 27.50508 10.058471 12.308402 22.04861 23.31357 67.81498 3.939915
## 1304 27.12947 24.06304 10.004453 11.728596 24.10621 21.72844 58.17726 5.943724
## 1305 24.81094 23.62678 9.365788 11.073955 17.51909 19.97281 59.27656 5.856331
## 1306 22.33892 23.77440 9.192797 11.689073 18.09591 20.75239 61.72486 5.325074
## 1307 23.72726 23.93945 15.923781 7.757090 27.17214 25.43076 34.25674 10.743218
## 1308 25.57028 25.88464 11.281775 12.009186 21.10553 22.98131 66.97481 4.216435
## 1309 24.28717 26.03423 10.982572 12.330284 20.82249 21.80276 67.91418 4.012897
## 1310 23.38032 25.96738 10.944685 11.589537 23.26258 20.96380 67.89808 4.021087
## 1311 22.97322 27.10505 8.885230 11.076750 16.22269 18.16059 62.27610 5.308453
## 1312 23.58751 24.29967 10.008384 10.705349 22.69601 20.23189 57.52131 6.161875
## 1313 26.18841 24.98712 10.995071 10.401308 20.49431 21.47300 48.32911 8.045088
## 1314 19.15281 19.06725 7.547668 11.758377 17.68614 16.26408 63.75547 5.158546
## 1315 23.92244 25.49845 9.999622 9.756697 21.55859 21.56077 55.90000 6.210000
## 1334 25.46251 26.64396 9.906633 10.453336 22.37117 22.84888 61.40000 4.100000
## 1353 22.09169 28.07379 9.665312 9.605007 20.07661 20.12716 47.20000 5.660000
## 1372 26.34456 23.49281 9.661908 9.225406 21.56845 22.03168 48.20000 12.400000
## 1391 24.33736 23.94627 12.576263 12.867410 20.08692 20.32090 65.29534 4.632881
## 1392 24.56416 24.18033 11.724569 10.427714 27.52816 26.40631 50.10000 7.080000
## 1411 26.30723 23.92448 7.985537 9.284697 19.19948 18.33022 41.90000 11.900000
## 1430 21.91255 28.09646 5.846103 10.089456 18.04099 19.42994 46.80000 10.900000
## 1449 26.67078 22.17432 8.544338 9.708748 19.40001 18.85483 41.60000 12.900000
## 1468 23.22055 25.97794 11.387807 11.285548 22.13123 21.26313 44.30000 6.690000
## 1487 24.99690 27.23902 10.488427 11.445105 22.62902 25.72357 32.60000 3.810000
## 1506 21.03695 22.26847 10.541307 9.678177 16.57747 17.42194 43.40000 5.480000
## 1525 23.67079 24.50357 8.477857 10.166476 17.26136 17.46136 46.30000 8.690000
## 1544 19.99873 23.04488 10.740533 11.861010 20.43164 17.80555 66.37226 4.474737
## 1545 29.54948 22.51975 10.484425 12.108359 20.85134 16.34527 31.60000 12.300000
## 1564 23.17187 25.18772 11.220518 9.548208 22.43535 22.25967 49.20000 9.760000
## 1583 21.21622 24.28532 10.960531 8.968065 23.16068 23.48999 53.40000 10.400000
## 1602 22.99591 24.24964 10.019037 8.531568 21.37614 20.82249 60.00000 5.260000
## 1621 25.42788 24.80184 8.590075 8.871211 17.57769 19.73392 47.60000 5.920000
## 1640 23.75737 20.88617 6.927890 13.408973 17.53509 16.57800 63.30710 5.162081
## 1641 26.10599 28.46406 10.098975 10.393635 23.04097 22.15808 50.60000 5.740000
## 1660 24.42321 27.33021 10.388094 8.474758 19.93831 21.28205 53.00000 5.560000
## 1679 23.58885 25.53393 10.990366 9.615567 19.35312 22.38159 43.09000 6.120000
## 1700 23.96642 25.84580 11.220712 10.047665 19.78065 22.52779 43.27000 7.155000
## 1721 19.91930 21.95239 5.077671 10.093173 14.29073 16.82870 42.08500 9.840000
## 1742 22.72406 24.52266 8.480967 11.148774 17.88449 19.81789 54.71000 7.000000
## 1763 22.78997 24.69268 9.292456 10.242361 18.14960 20.71082 49.70000 6.950000
## F_Div_Treg F_Treg17 F_Th1 F_Div_Th1 F_Th17 F_Div_Th17
## 1 16.2050000 13.520000 6.78000000 71.20000000 0.8900000 46.8750000
## 22 21.3650000 11.565000 10.92000000 75.11500000 1.0750000 42.3900000
## 43 12.4550000 9.505000 2.96500000 19.84000000 1.6300000 30.0550000
## 64 23.7600000 12.780000 9.25000000 81.21000000 1.7050000 78.3050000
## 85 13.4650000 14.400000 2.54500000 27.85000000 1.0600000 27.4450000
## 106 13.3550000 7.035000 2.90000000 25.52000000 0.6950000 32.1950000
## 127 24.7950000 13.950000 6.87000000 76.51500000 1.1100000 65.7350000
## 148 17.1150000 8.645000 9.58500000 51.87000000 1.0900000 40.6000000
## 169 21.0000000 14.540000 7.02000000 67.36000000 1.6150000 65.0550000
## 190 13.0900000 6.825000 7.71000000 79.02000000 1.1850000 55.8350000
## 211 14.1100000 14.350000 1.73000000 14.31000000 0.9250000 33.0750000
## 232 20.5150000 9.260000 9.10000000 64.37000000 0.8050000 49.9100000
## 253 7.8500000 9.015000 2.50500000 19.19000000 0.9450000 28.8150000
## 274 16.7750000 13.315000 4.84000000 54.63500000 0.9700000 35.2750000
## 295 12.7100000 9.660000 1.87500000 29.57500000 0.5350000 21.1550000
## 316 12.1100000 7.535000 1.45500000 21.43500000 0.5500000 22.9200000
## 337 24.1100000 8.970000 11.54000000 90.78000000 4.0500000 67.7800000
## 358 13.0050000 9.130000 1.83500000 22.30000000 1.0750000 30.8900000
## 379 16.5750000 15.280000 4.44500000 48.20500000 0.7950000 28.3550000
## 400 15.7950000 4.280000 3.71000000 75.72000000 0.7650000 46.7200000
## 421 41.6050000 11.280000 6.79500000 59.59000000 1.2250000 36.9600000
## 442 8.2600000 4.370000 1.53500000 22.66500000 0.5800000 19.2300000
## 463 38.2100000 8.875000 5.92500000 65.70000000 1.9350000 41.4550000
## 484 23.5250000 7.885000 3.54000000 53.20000000 1.3600000 24.0450000
## 505 10.5500000 4.220000 1.42500000 22.07500000 1.0700000 31.6650000
## 526 36.5850000 17.105000 3.37000000 72.07500000 0.6200000 38.0400000
## 547 16.8350000 13.005000 1.73500000 11.91000000 1.1200000 50.0700000
## 568 13.0000000 12.720000 1.85500000 13.03500000 1.4400000 19.1200000
## 589 30.5800000 17.135000 5.61500000 41.68000000 0.9750000 22.3550000
## 610 43.8550000 12.800000 5.39500000 56.13000000 0.8750000 30.4600000
## 631 8.2250000 10.045000 1.78000000 31.14500000 1.1100000 63.2350000
## 652 22.1500000 12.340000 1.83500000 34.18000000 1.0100000 12.9050000
## 673 31.7950000 18.210000 2.74000000 21.99000000 0.7300000 27.2750000
## 694 19.2450000 7.590000 3.11000000 35.55500000 1.4350000 39.9950000
## 715 31.5950000 9.750000 3.05500000 29.22000000 0.8400000 30.1700000
## 736 17.7300000 12.165000 1.51000000 28.17000000 0.6600000 9.7000000
## 757 19.5500000 6.445000 1.30500000 27.14000000 0.4850000 19.2000000
## 778 52.6200000 14.605000 7.42500000 79.50500000 1.7300000 69.7000000
## 799 36.4750000 18.505000 5.28000000 48.67000000 1.9400000 24.2200000
## 820 26.9400000 8.940000 3.02000000 22.30500000 1.4000000 21.8050000
## 841 19.4950000 6.415000 1.37500000 27.52000000 0.8300000 28.2850000
## 862 36.7750000 9.390000 4.13000000 60.85500000 0.6800000 27.7100000
## 883 34.9950000 6.330000 2.81000000 76.26500000 0.6350000 46.6900000
## 904 12.9050000 5.325000 1.33000000 22.60000000 0.6300000 23.0550000
## 925 35.2350000 8.230000 5.48000000 76.18500000 1.4300000 59.0400000
## 946 13.7200000 5.700000 1.23500000 29.35000000 0.5900000 20.9100000
## 967 22.7750000 17.040000 1.83500000 15.25500000 1.0800000 12.2200000
## 988 25.7925153 10.277050 4.50541369 54.56648742 1.0270539 36.9829471
## 989 33.9800000 5.645000 4.17000000 58.70500000 0.5200000 39.0650000
## 1010 9.2234698 9.239743 -0.45538458 6.58905175 0.6842821 9.6370752
## 1011 11.2134851 9.582648 0.57373710 12.29371706 0.8989550 14.4335789
## 1012 9.0943922 8.771985 -1.40636741 6.33664696 0.3162953 6.2401996
## 1013 10.1740304 9.538581 0.30421796 9.27831927 0.8941468 12.8635495
## 1014 5.6354108 8.511990 -2.52821773 -3.66773273 0.2102112 0.2305219
## 1015 16.7498936 9.209124 0.80207653 28.51508990 0.4411832 18.5831541
## 1016 9.8579970 9.033281 -0.75402050 8.49138514 0.5017586 8.9791606
## 1017 11.2215137 9.280541 -0.02445842 12.39685272 0.6586300 12.3508776
## 1018 17.4979083 10.274588 3.04775290 30.41213001 1.2661917 26.8730236
## 1019 13.5711782 9.017313 -0.13536101 19.30888204 0.3811395 13.3867569
## 1020 6.5397041 8.857508 -1.68407328 -1.12552495 0.4585178 3.7240095
## 1021 8.4559290 9.070628 -0.92546578 4.39851582 0.5721917 7.5317957
## 1022 26.7000000 7.630000 8.13000000 60.60000000 3.7000000 62.1000000
## 1043 34.5000000 11.500000 13.10000000 63.50000000 3.1600000 64.2000000
## 1064 25.6000000 9.050000 4.78000000 54.90000000 2.1700000 42.7000000
## 1085 8.0700000 3.230000 4.83000000 15.80000000 1.5300000 13.3000000
## 1106 24.9000000 8.360000 11.60000000 54.60000000 3.0300000 43.8000000
## 1127 30.6000000 12.100000 6.87000000 63.10000000 3.7900000 65.8000000
## 1148 23.2000000 9.410000 9.08000000 49.70000000 2.0600000 52.4000000
## 1169 13.6000000 17.500000 5.73000000 19.40000000 2.3500000 12.4000000
## 1190 30.0000000 20.000000 12.40000000 58.70000000 3.0300000 58.0000000
## 1211 21.6000000 10.500000 2.70000000 27.50000000 1.5100000 54.3000000
## 1232 41.2000000 8.040000 6.85000000 83.70000000 1.1900000 73.9000000
## 1253 45.1000000 5.680000 7.26000000 70.20000000 1.4500000 47.7000000
## 1274 10.8439750 9.143735 -0.36210720 11.33352560 0.5608805 10.9439328
## 1275 6.4800000 3.430000 3.26000000 12.60000000 1.0000000 9.2000000
## 1296 16.4161860 10.534150 3.37345277 27.19348619 1.5039131 27.3545739
## 1297 9.5128330 8.758138 -1.36056058 7.55885808 0.2931285 6.6534531
## 1298 11.1450308 8.880784 -0.83126606 12.27965884 0.3431563 9.4889901
## 1299 35.5670557 12.815999 11.25653524 82.36098531 2.7607086 66.4620329
## 1300 11.2486247 9.031337 -0.51431457 12.54159262 0.4597932 10.6578112
## 1301 13.6429182 9.040063 -0.07764333 19.51179282 0.3971343 13.6316223
## 1302 0.6843582 8.431735 -3.55466517 -18.06467458 0.2903394 -6.3497864
## 1303 3.5896149 8.736471 -2.44099856 -9.68462684 0.4480752 -0.7039911
## 1304 12.3295266 9.600071 0.80378829 15.53918000 0.8803622 15.9122536
## 1305 16.1653487 9.518729 1.31417769 26.73108238 0.7042240 20.0162810
## 1306 13.1843463 9.296644 0.35128419 18.10863336 0.6143744 14.8507789
## 1307 28.0683141 11.722360 7.77257039 60.81236170 2.1095281 49.7627371
## 1308 7.8378952 8.824135 -1.52293404 2.66379168 0.3942624 5.0725031
## 1309 6.7042510 8.738962 -1.89053573 -0.61504663 0.3595236 3.1031493
## 1310 6.8846005 8.740993 -1.85491615 -0.09038093 0.3558960 3.3366690
## 1311 16.0390445 9.259162 0.77688453 26.43179232 0.5016110 18.0647658
## 1312 15.7237101 9.668789 1.53465643 25.40535608 0.8363176 20.5182543
## 1313 23.1021534 10.489068 4.45500524 46.67582097 1.2737491 35.1778112
## 1314 20.0953875 9.145769 1.26228600 38.27434221 0.2935918 22.2151335
## 1315 26.4000000 17.500000 5.01000000 44.10000000 1.4700000 29.7000000
## 1334 21.4000000 15.500000 1.46000000 33.80000000 0.9900000 17.0000000
## 1353 30.2000000 18.500000 6.80000000 63.40000000 1.5200000 47.9000000
## 1372 17.9000000 7.520000 3.99000000 52.90000000 2.2000000 36.6000000
## 1391 11.6635824 8.982804 -0.53796184 13.76281785 0.4091612 10.8265767
## 1392 22.2000000 14.200000 4.95000000 59.50000000 1.0700000 23.7000000
## 1411 22.2000000 5.660000 4.86000000 55.80000000 1.2600000 26.5000000
## 1430 24.1000000 5.860000 4.20000000 66.30000000 1.5200000 48.0000000
## 1449 23.0000000 6.090000 3.80000000 56.50000000 2.1600000 35.9000000
## 1468 40.9000000 11.000000 6.35000000 71.90000000 1.4700000 56.2000000
## 1487 43.2000000 13.500000 4.17000000 53.80000000 4.8100000 11.1000000
## 1506 24.9000000 13.100000 5.66000000 62.70000000 1.3200000 36.1000000
## 1525 32.7000000 13.300000 9.29000000 51.80000000 1.2800000 27.1000000
## 1544 12.9382851 8.894299 -0.49035912 17.49828768 0.3017737 11.7646302
## 1545 26.1000000 4.030000 6.46000000 81.70000000 1.2300000 46.3000000
## 1564 15.3000000 6.320000 2.26000000 29.60000000 1.3900000 26.3000000
## 1583 14.3000000 4.680000 1.58000000 43.20000000 1.5200000 37.1000000
## 1602 16.0000000 9.450000 3.04000000 26.10000000 0.7800000 15.1000000
## 1621 24.3000000 13.400000 5.75000000 46.10000000 1.1200000 31.9000000
## 1640 17.4315703 9.175042 0.85382679 30.50922132 0.3942837 19.1765585
## 1641 18.5000000 7.520000 2.02000000 20.70000000 1.3100000 15.3000000
## 1660 21.9000000 12.800000 4.38000000 41.90000000 1.4100000 25.8000000
## 1679 21.8850000 25.480000 7.62000000 60.78000000 1.4150000 45.3250000
## 1700 16.3650000 10.450000 5.48500000 65.42500000 1.1700000 29.2700000
## 1721 37.8500000 8.350000 7.57000000 71.14000000 1.0050000 41.1050000
## 1742 17.5700000 9.180000 1.31500000 26.47500000 0.9250000 25.8150000
## 1763 30.0000000 19.500000 5.04000000 62.20000000 1.4100000 42.0000000
## F_CD8 F_Act_CD8 F_Div_Act_CD8 F_IFNy_CD4 F_IFNy_CD8
## 1 14.390000 11.5000000 49.52000000 4.91500000 21.740000
## 22 13.840000 13.2050000 59.09000000 9.08500000 27.535000
## 43 10.020000 10.9150000 11.53500000 3.04500000 41.360000
## 64 25.305000 11.1050000 55.93500000 9.08500000 38.165000
## 85 17.550000 9.8150000 12.83000000 2.00500000 19.390000
## 106 7.490000 5.3950000 21.31000000 2.79500000 19.230000
## 127 9.065000 8.9000000 55.69000000 8.45500000 34.310000
## 148 13.995000 9.2000000 55.97000000 8.75500000 28.690000
## 169 8.840000 8.3750000 45.89500000 12.91000000 46.265000
## 190 26.505000 18.2600000 38.45000000 4.59000000 27.800000
## 211 13.900000 3.7850000 8.98500000 1.69000000 13.755000
## 232 31.115000 13.4600000 38.51500000 9.60000000 30.505000
## 253 18.080000 3.4550000 8.71000000 1.95000000 13.490000
## 274 19.235000 4.9300000 44.24000000 4.35500000 23.725000
## 295 17.080000 4.7550000 15.41000000 1.81000000 11.825000
## 316 28.360000 5.6400000 6.33500000 1.65000000 16.100000
## 337 24.175000 20.5000000 29.36500000 3.24000000 27.110000
## 358 11.410000 4.4550000 12.67500000 2.58000000 22.560000
## 379 17.805000 7.6300000 39.93000000 4.84500000 26.830000
## 400 33.620000 13.3850000 33.36500000 1.74000000 16.375000
## 421 12.140000 10.9100000 47.47500000 2.62000000 16.955000
## 442 26.665000 4.7400000 7.56000000 1.76000000 14.625000
## 463 35.575000 19.1750000 31.74500000 3.05500000 19.105000
## 484 17.865000 11.1250000 29.02000000 2.90000000 23.535000
## 505 27.880000 6.6150000 10.91000000 1.11000000 20.565000
## 526 27.135000 6.9450000 43.53500000 2.01500000 11.530000
## 547 18.020000 2.3650000 6.81500000 1.13000000 8.335000
## 568 14.640000 4.7650000 7.74000000 1.82500000 15.605000
## 589 7.365000 16.4150000 45.83000000 5.47500000 31.365000
## 610 13.720000 7.8450000 51.61000000 5.17000000 21.410000
## 631 20.855000 3.8550000 10.13000000 1.36000000 8.335000
## 652 12.335000 3.9850000 23.61000000 1.22500000 10.585000
## 673 18.260000 2.8100000 15.01500000 2.01000000 8.880000
## 694 26.645000 17.7350000 27.74500000 3.21500000 34.270000
## 715 7.725000 6.5000000 18.93000000 3.60500000 22.265000
## 736 21.500000 3.3250000 12.07500000 0.41000000 3.605000
## 757 27.155000 3.9000000 6.50000000 1.02000000 7.420000
## 778 21.090000 21.6050000 36.21000000 2.31500000 14.775000
## 799 18.575000 8.1350000 46.22000000 2.31000000 17.460000
## 820 10.375000 6.7200000 17.13500000 2.78000000 18.350000
## 841 29.465000 4.2200000 16.69500000 0.83000000 9.825000
## 862 24.340000 7.4100000 46.67000000 1.32500000 4.500000
## 883 28.860000 7.4600000 43.70000000 1.45500000 7.310000
## 904 33.330000 8.9100000 6.91500000 0.40000000 5.010000
## 925 34.585000 15.0350000 35.20500000 1.54000000 9.265000
## 946 32.530000 7.5800000 9.96000000 0.43000000 4.315000
## 967 14.995000 5.1600000 6.56500000 1.07000000 9.730000
## 988 23.845654 11.7349682 34.78714928 2.81001790 17.185952
## 989 28.025000 12.9850000 49.65000000 2.52000000 14.905000
## 1010 19.464310 1.5948087 2.14725525 -0.35490981 9.380939
## 1011 17.893490 3.0858048 5.62848650 0.44754326 12.142309
## 1012 23.845528 0.9407591 2.81722605 -1.26879078 5.479772
## 1013 17.416839 2.4759454 3.53859192 0.28963135 11.828174
## 1014 23.348170 -1.2304664 -3.90938096 -2.01354790 3.487428
## 1015 26.274581 5.5731717 17.98276054 0.11201408 8.733962
## 1016 21.996798 1.6751572 3.89222262 -0.70994259 7.623081
## 1017 20.802276 2.7121546 6.25274092 -0.13630794 9.617946
## 1018 16.688055 7.3052620 17.40819095 2.22540068 17.596489
## 1019 25.364950 3.6368139 11.70644584 -0.48125336 7.296685
## 1020 20.812274 -0.3156260 -2.70886647 -1.28194259 6.327048
## 1021 20.424202 0.9736284 0.87866642 -0.73571271 8.007961
## 1022 6.580000 11.4000000 24.40000000 5.82000000 38.300000
## 1043 9.980000 16.2000000 22.80000000 8.40000000 37.700000
## 1064 8.930000 12.4000000 30.60000000 2.85000000 23.700000
## 1085 15.400000 13.7000000 6.07000000 3.05000000 21.500000
## 1106 7.770000 19.5000000 26.50000000 9.34000000 36.900000
## 1127 5.870000 12.8000000 16.60000000 3.91000000 28.900000
## 1148 6.140000 20.5000000 22.50000000 9.13000000 50.100000
## 1169 14.700000 3.3700000 11.80000000 6.59000000 7.210000
## 1190 7.300000 10.2000000 23.50000000 9.70000000 21.500000
## 1211 10.500000 7.5200000 7.41000000 2.72000000 20.300000
## 1232 7.560000 26.5000000 42.50000000 3.11000000 22.000000
## 1253 5.790000 25.9000000 62.70000000 2.70000000 14.500000
## 1274 21.789482 2.3395272 5.73656000 -0.42734645 8.494623
## 1275 11.500000 7.3700000 8.52000000 1.11000000 20.100000
## 1296 13.258358 7.0526841 14.61922374 2.65189025 19.821210
## 1297 24.340803 1.1467486 3.72203830 -1.26632424 5.342343
## 1298 24.575859 2.1712423 6.89621519 -0.91496768 6.282157
## 1299 7.920738 20.1276186 50.16780110 8.40481967 37.889540
## 1300 23.219438 2.4148690 6.81062062 -0.61648781 7.534563
## 1301 25.208540 3.7035599 11.81105732 -0.43222939 7.483021
## 1302 19.832564 -3.9731201 -14.12447452 -2.51491426 3.074261
## 1303 19.420767 -2.0414326 -8.64832685 -1.72231667 5.469174
## 1304 18.692375 3.7032046 7.93246456 0.55926688 12.229864
## 1305 22.794646 5.6485288 16.13516358 0.67006622 11.350928
## 1306 22.346976 3.7798136 10.33408651 0.03205768 9.650455
## 1307 11.933296 14.7575857 36.65078905 5.76500388 29.142490
## 1308 22.256764 0.3354380 0.07899296 -1.25574638 5.980768
## 1309 22.093408 -0.3761121 -2.12565440 -1.49976164 5.328105
## 1310 22.230037 -0.2773227 -1.75176086 -1.48322408 5.335703
## 1311 25.178521 5.2564058 16.39234966 0.15911567 9.188945
## 1312 20.970906 5.6005627 14.90785586 0.92947805 12.627560
## 1313 19.479906 10.5644231 28.72237341 3.03208182 19.097084
## 1314 29.779567 7.2793216 25.12165996 0.22333100 8.030783
## 1315 14.400000 14.4000000 29.10000000 2.87000000 23.500000
## 1334 16.400000 4.3700000 11.60000000 0.34000000 16.200000
## 1353 15.600000 11.2000000 38.90000000 2.84000000 18.200000
## 1372 26.100000 14.0000000 38.10000000 1.67000000 21.100000
## 1391 24.044876 2.5756065 7.77787573 -0.68136486 7.107525
## 1392 13.800000 11.2000000 43.00000000 2.24000000 35.600000
## 1411 27.900000 13.3000000 54.10000000 1.85000000 12.200000
## 1430 28.400000 13.9000000 41.80000000 2.60000000 23.500000
## 1449 25.200000 10.7000000 44.30000000 2.05000000 15.100000
## 1468 13.900000 20.9000000 52.20000000 2.92000000 31.400000
## 1487 14.400000 12.1000000 28.80000000 1.96000000 25.100000
## 1506 14.500000 18.6000000 40.20000000 1.89000000 16.700000
## 1525 13.900000 19.4000000 32.90000000 6.73000000 28.300000
## 1544 25.998592 3.1451651 10.62735869 -0.76346133 6.301866
## 1545 23.800000 20.9000000 48.60000000 2.36000000 8.070000
## 1564 23.300000 14.1000000 15.50000000 1.54000000 18.200000
## 1583 24.500000 13.4000000 16.20000000 1.32000000 16.900000
## 1602 17.500000 8.3800000 7.74000000 1.70000000 14.500000
## 1621 19.100000 11.5000000 27.00000000 3.97000000 32.000000
## 1640 27.192125 5.8943294 19.47995061 0.09373862 8.413797
## 1641 11.700000 7.1100000 7.55000000 0.75000000 24.400000
## 1660 15.000000 7.4700000 33.40000000 2.13000000 22.100000
## 1679 16.055000 7.8150000 60.25500000 8.38000000 29.545000
## 1700 10.565000 11.4300000 47.35500000 3.41500000 26.765000
## 1721 30.975000 27.8050000 38.40000000 3.78500000 12.825000
## 1742 26.945000 9.6650000 10.63000000 0.66500000 7.805000
## 1763 14.800000 10.9000000 41.40000000 1.06000000 10.300000
Caution: When imputing data, the percentages of inertia associated with the first dimensions will be overestimated.
Another problem: the imputed data are, when the pca is performed considered like real observations. But they are estimations!!
Visualizing uncertainty due to issing data:
–> mulrimple imputation: generate several plausible values for each missing data point
We here visualize the variability, that is uncertainty on the plane
defined by two pca axes.
## $PlotIndProc
##
## $PlotDim
##
## $PlotIndSupp
##
## $PlotVar
Individuals lying on the axis have no missing data, but individuals that
far away have many missing data. big ellipse = big uncertainty tight
elipse (line) = low uncertainty
Variable representation: Poins tight together )look like one) - have no missing variables –> low uncertainty Points spread – > higher variability – > higher uncertainty
High uncertainty–> we should interpret the result with care
The individuals with many missing data values make the axes move, and thus the positions of all individuals
Therefore in the last plots every individual is getting an eclipse as they are as well influenced by the missing data of the others.
THe plot with the dimensions shows the projections of the pca dimensions of each imputed table on the pca plane obtained using the original imputed data table
As all of the arrows are close to either the first or second axes, this means that the axes are stable with respect to the set of imputed tables –> we don’t have evidence of instability here.
The total contribution to PC1 and PC2 is obtained with the following R
code:
##
## Call:
## lm(formula = max_WL ~ pc1 + pc2 + challenge_infection, data = i)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.3918 -2.9882 0.1399 3.3999 14.5286
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 91.4040 0.7929 115.273 < 2e-16 ***
## pc1 0.3241 0.1528 2.121 0.036 *
## pc2 -0.3118 0.1999 -1.559 0.122
## challenge_infectionE88 -6.3572 1.4003 -4.540 1.38e-05 ***
## challenge_infectionUNI 5.3304 1.2172 4.379 2.62e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.288 on 116 degrees of freedom
## Multiple R-squared: 0.3672, Adjusted R-squared: 0.3453
## F-statistic: 16.83 on 4 and 116 DF, p-value: 6.65e-11
## [1] 753.3354
##
## Call:
## lm(formula = max_WL ~ pc1 + pc2, data = i)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.564 -3.091 1.954 5.027 8.267
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 92.36267 0.59853 154.315 <2e-16 ***
## pc1 0.02925 0.18460 0.158 0.874
## pc2 0.10769 0.21803 0.494 0.622
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.584 on 118 degrees of freedom
## Multiple R-squared: 0.002275, Adjusted R-squared: -0.01464
## F-statistic: 0.1345 on 2 and 118 DF, p-value: 0.8743
## df AIC
## weight_lm 6 753.3354
## weight_lm_exp_only 4 804.4239